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Expert-verified 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. 124 is the ___?__ term of -2, 5, 12, ... .

124 is the 19th term of the arithmetic sequence -2, 5, 12, … .

See the step by step solution

## Step 1. Given Information.

Given arithmetic sequence is -2, 5, 12, ...

## 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 $5-\left(-2\right)=5+2=7$

The difference between the second two terms is $12-5=7$

The common difference is $d=7$

The given nth term is ${a}_{n}=124$

Plugging the values in the formula:

$\begin{array}{l}{a}_{n}={a}_{1}+\left(n-1\right)d\\ 124=-2+\left(n-1\right)\left(7\right)\\ 124+2=\left(n-1\right)\left(7\right)\\ \left(n-1\right)\left(7\right)=126\\ n-1=\frac{126}{7}\\ n-1=18\\ n=18+1\\ n=19\end{array}$

## Step 3. Conclusion.

Hence, 124 is the 19th term of the arithmetic sequence -2, 5, 12, … . ### Want to see more solutions like these? 