Question

Find the indicated term of each arithmetic sequence.

$a_{12}$ for 8, 3, -2, …

Short answer

The indicated term of the arithmetic sequence is-47.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is 8, 3, -2, …

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 $a_1=8$

The difference between the first two terms is $3-8=-5$

The difference between the next two terms is $-2-3=-5$

The common difference is $d=-5$

And the required term is $n=12$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{12}=8+(12-1)(-5)\\ a_{12}=8+\left(11\right)(-5)\\ a_{12}=8-55\\ a_{12}=-47\end{array}$

Step 3. Conclusion.

Hence, the indicated term of the arithmetic sequence is -47.