## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 34

#### Answer

$a_n=8n+17$

#### Work Step by Step

We know that the general formula of an arithmetic sequence is given by $a_n= a_1+(n-1) d$ ...(1) For $n=9$ and $n=15$ we have $a_9=a_1+8d$ ..(2) $a_{15}=a_1+14d$ ..(3) Now, we have $a_{15}-a_9=(a_1+14d)-(a_1+8d)$ This gives: $137-89=6d \implies d=\dfrac{48}{6}=8$ $a_9=a_1+8d \implies a_1 =a_9-8d=89-(8)(8)=25$ From equation (1) we have $a_n=25+(n-1) 8=25+8n-8$ Thus, $a_n=8n+17$

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