messages listlengths 3 3 | topic stringclasses 6
values | subtopic stringclasses 134
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{47}{39}$, and $a_n=a_{n-1}+-10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{19}{46}$, and $a_n=a_{n-1}+-\\frac{18}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{4}{5}$, and $a_n=a_{n-1}+-10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=21$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{37}{43}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{43}{27}$, and $a_n=a_{n-1}+-7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=5$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{7}{33}$, and $a_n=a_{n-1}+-\\frac{1}{\\sqrt{2}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{8}{3}$, and $a_n=a_{n-1}+\\frac{21}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{13}{31}$, and $a_n=a_{n-1}+9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=28$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{63}{38}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=7$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{49}{94}$, and $a_n=a_{n-1}+\\frac{2}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{36}{19}$, and $a_n=a_{n-1}+-\\frac{21}{4}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$,... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{20}$, and $a_n=a_{n-1}+-7 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{15}{8}$, and $a_n=a_{n-1}+7 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{58}{95}$, and $a_n=a_{n-1}+-\\frac{16}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{9}{10}$, and $a_n=a_{n-1}+-\\frac{48}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{5}{49}$, and $a_n=a_{n-1}+-\\frac{61}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{3}{86}$, and $a_n=a_{n-1}+7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=16$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{13}{18}$, and $a_n=a_{n-1}+2 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{46}{7}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=29$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{91}{67}$, and $a_n=a_{n-1}+\\frac{19}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{9}{13}$, and $a_n=a_{n-1}+-2 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{7}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=17$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{28}{11}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{3}{8}$, and $a_n=a_{n-1}+-\\frac{33}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{13}{35}$, and $a_n=a_{n-1}+8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{44}{73}$, and $a_n=a_{n-1}+\\frac{1}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{9}{77}$, and $a_n=a_{n-1}+-\\frac{13}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{47}{85}$, and $a_n=a_{n-1}+-4 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{11}{47}$, and $a_n=a_{n-1}+-5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=28... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{67}{93}$, and $a_n=a_{n-1}+2$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{6}{11}$, and $a_n=a_{n-1}+\\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{14}{3}$, and $a_n=a_{n-1}+-\\frac{4}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{53}{90}$, and $a_n=a_{n-1}+\\frac{45}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{83}{17}$, and $a_n=a_{n-1}+3 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{7}{2}$, and $a_n=a_{n-1}+-\\frac{10}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{10}{7}$, and $a_n=a_{n-1}+7$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=24$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{82}{45}$, and $a_n=a_{n-1}+-2 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-4$, and $a_n=a_{n-1}+\\frac{4}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{53}{30}$, and $a_n=a_{n-1}+\\frac{13}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{1}{40}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{71}{81}$, and $a_n=a_{n-1}+\\frac{2}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{11}{17}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=12$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{81}{28}$, and $a_n=a_{n-1}+\\frac{8}{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{5}{26}$, and $a_n=a_{n-1}+2 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{54}{83}$, and $a_n=a_{n-1}+-\\frac{9}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{83}{84}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{64}{25}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=17$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{95}{18}$, and $a_n=a_{n-1}+5 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{5}{43}$, and $a_n=a_{n-1}+\\frac{11}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{32}{47}$, and $a_n=a_{n-1}+4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{2}{3}$, and $a_n=a_{n-1}+8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27$."
... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{18}{79}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=10$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=36$, and $a_n=a_{n-1}+\\frac{21}{4}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=13$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{81}{47}$, and $a_n=a_{n-1}+5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=16$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{17}{66}$, and $a_n=a_{n-1}+-5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=18... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{65}{44}$, and $a_n=a_{n-1}+2 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, whe... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{30}{13}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=10$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{37}{27}$, and $a_n=a_{n-1}+-12$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=1... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{9}{55}$, and $a_n=a_{n-1}+2 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{47}{45}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{47}{25}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=4$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{8}{9}$, and $a_n=a_{n-1}+5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=17$."
... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{8}{3}$, and $a_n=a_{n-1}+7 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wher... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{5}{6}$, and $a_n=a_{n-1}+-2$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=28$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{41}{19}$, and $a_n=a_{n-1}+-\\frac{27}{4}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$,... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{98}$, and $a_n=a_{n-1}+-3 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{45}{16}$, and $a_n=a_{n-1}+-4 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{13}{24}$, and $a_n=a_{n-1}+9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=17$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{41}{3}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=11$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{8}{9}$, and $a_n=a_{n-1}+-\\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=1... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{5}{54}$, and $a_n=a_{n-1}+-10$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=14... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{21}{10}$, and $a_n=a_{n-1}+\\frac{8}{\\sqrt{3}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{41}{2}$, and $a_n=a_{n-1}+8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=27$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{85}{46}$, and $a_n=a_{n-1}+-4$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=11$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{53}{67}$, and $a_n=a_{n-1}+3 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{15}{28}$, and $a_n=a_{n-1}+-5 \\sqrt{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{33}{10}$, and $a_n=a_{n-1}+3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=8$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{25}$, and $a_n=a_{n-1}+-\\frac{17}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{47}{73}$, and $a_n=a_{n-1}+-\\frac{21}{\\sqrt{5}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{22}{71}$, and $a_n=a_{n-1}+-3$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=29$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{1}{5}$, and $a_n=a_{n-1}+\\frac{17}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{88}{37}$, and $a_n=a_{n-1}+-3 \\sqrt{3}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{77}{34}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{96}{91}$, and $a_n=a_{n-1}+\\frac{23}{7}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{58}{99}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=21$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-68$, and $a_n=a_{n-1}+\\frac{7}{\\sqrt{2}}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{19}{18}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=19$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{5}{7}$, and $a_n=a_{n-1}+-8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=25$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{49}{26}$, and $a_n=a_{n-1}+6$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=6$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{8}{31}$, and $a_n=a_{n-1}+5$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=3$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=0$, and $a_n=a_{n-1}+-\\frac{37}{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=24$.... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{7}{99}$, and $a_n=a_{n-1}+8$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=6$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{89}{77}$, and $a_n=a_{n-1}+9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=23$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{47}{9}$, and $a_n=a_{n-1}+2$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=5$."
... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{78}{7}$, and $a_n=a_{n-1}+0$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=11$."... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{31}{98}$, and $a_n=a_{n-1}+3 \\sqrt{5}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, wh... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{77}{53}$, and $a_n=a_{n-1}+9$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=10$... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{67}{87}$, and $a_n=a_{n-1}+-\\frac{7}{4}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, w... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{91}{45}$, and $a_n=a_{n-1}+-2 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where $... | algebra | arithmetic_series |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Consider the arithmetic sequence defined by $a_1=-\\frac{56}{93}$, and $a_n=a_{n-1}+\\frac{13}{2}$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, ... | algebra | arithmetic_series |
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