## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 11 - Review Exercises - Page 841: 70

#### Answer

$n(72-4n)$

#### Work Step by Step

$a_3-a_2=52-60=a_2-a_1=60-68=-8=d$, thus this is an arithmetic sequence with a common difference of $-8$ The nth term of an arithmetic sequence can be obtained by the following formula: $a_n=a_1+(n-1)d$, where $a_1$ is the first term and $d$ is the common difference. The sum of the first $n$ terms of an arithmetic sequence can be obtained by the following formula: $\frac{n(a_1+a_n)}{2},$ where $a_1$ is the first term, $a_n$ is the nth term and $n$ is the number of terms. Thus the sum:$\frac{n(a_1+a_n)}{2}=\frac{n(a_1+a_1+(n-1)d)}{2}=\frac{n(68+68+(n-1)(-8))}{2}=\frac{n(136-8n+8)}{2}=\frac{n(144-8n)}{2}=n(72-4n)$

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