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Expert-verified Found in: Page 581 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # 68 is the ___?__ th term of the arithmetic sequence -2, 3, 8, ... .

68 is the 15th term of the arithmetic sequence -2, 3, 8, ....

See the step by step solution

## Step 1. Given Information.

Given arithmetic sequence is -2, 3, 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 ${a}_{1}=-2$

The difference between the first two terms is $3-\left(-2\right)=3+2=5$

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

The common difference is $d=5$

The given nth term is ${a}_{n}=68$

Plugging the values in the formula:

$\begin{array}{l}{a}_{n}={a}_{1}+\left(n-1\right)d\\ 68=-2+\left(n-1\right)\left(5\right)\\ 68+2=\left(n-1\right)\left(5\right)\\ \left(n-1\right)\left(5\right)=70\\ n-1=\frac{70}{5}\\ n-1=14\\ n=14+1\\ n=15\end{array}$

## Step 3. Conclusion.

Hence, 68 is the 15th term of the arithmetic sequence -2, 3, 8, ... . ### Want to see more solutions like these? 