Question

Find the $a_{13}$ for the arithmetic sequence -17, -12, -7, ….

Short answer

The $a_{13}$ for the arithmetic sequence is43.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is -17, -12, -7, ….

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Here the first term is $a_1=-17$

The difference between the first two terms is $-12-(-17)=-12+17=5$

The difference between the next two terms is $-7-(-12)=-7+12=5$

Hence, the common difference is $d=5$

And the required term is $n=13$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{13}=-17+(13-1)\left(5\right)\\ a_{13}=-17+\left(12\right)\left(5\right)\\ a_{13}=-17+60\\ a_{13}=43\end{array}$

Step 3. Conclusion.

Hence, the $a_{13}$ for the arithmetic sequence is 43.