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Q38.

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Found in: Page 581

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Find the indicated term of each arithmetic sequence.${a}_{12}$ for 8, 3, -2, …

The indicated term of the arithmetic sequence is -47.

See the step by step solution

## Step 1. Given Information.

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

## Step 2. Calculation.

The nth term of an arithmetic sequence is given by ${a}_{n}={a}_{1}+\left(n-1\right)d$ .

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:

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

## Step 3. Conclusion.

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