Math Problem Solver

$$-104,-91,-78,-65,...$$ The sum of the first 17 terms in this arithmetic sequence is $0$.

The nth term in this sequence is given by the formula:

Explicit Formula: $$a_n=13 n - 117$$

Recursive Formula: $$a_n=a_{n-1} + 13, \text{where } a_1=-104$$

Summation Formula:

Option 1:

$$S_n=\frac{n}{2} (2 a_1 + (n - 1) d)$$ where $a_1$ is the 1^st term, $d$ is the common difference, and $n$ is the is the term number.

Option 2:

$$S_n=n \left(\frac{a_1 + a_n}{2}\right)$$ where $a_1$ is the 1^st term, $a_n$ is the n^th term, and $n$ is the is the term number.

Option 3:

$$\begin{aligned} S_n&=\sum_{i=1}^{n} a_{i} \\ &=\sum_{i=1}^{n} \left(13 i - 117\right) \\ &=\frac{13 n \left(n - 17\right)}{2} \end{aligned}$$where $n$ is the is the term number.