College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Review Exercises - Page 679: 20

Answer

See below.

Work Step by Step

The difference between two terms with an index difference of $13$ is $65$, thus $d=65/13=5$. Thus $a_1=a_{7}-(7-1)d=31-6(5)=1$. 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. Hence here: $d=5,a_1=1,a_{n}=1+(n-1)(5)=-4+5n$
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