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Found in: Page 582

### Algebra 2

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

# Complete the statement for each arithmetic sequence. 170 is the ___?__ term of -4, 2, 8, ... .

170 is the 30th term of the arithmetic sequence -4, 2, 8, … .

See the step by step solution

## Step 1. Given Information.

Given arithmetic sequence is -4, 2, 8, ...

## 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 ${a}_{1}=-4$

The difference between the first two terms is $2-\left(-4\right)=2+4=6$

The difference between the second two terms is $8-2=6$

The common difference is $d=6$

The given nth term is ${a}_{n}=170$

Plugging the values in the formula:

$\begin{array}{l}{a}_{n}={a}_{1}+\left(n-1\right)d\\ 170=-4+\left(n-1\right)\left(6\right)\\ 170+4=\left(n-1\right)\left(6\right)\\ \left(n-1\right)\left(6\right)=174\\ n-1=\frac{174}{6}\\ n-1=29\\ n=29+1\\ n=30\end{array}$

## Step 3. Conclusion.

Hence, 170 is the 30th term of the arithmetic sequence -4, 2, 8, … .