Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 859: 20

Answer

$a_n=5n-4$,

Work Step by Step

1. Start with a general form $a_n=a_1+(n-1)d$, based on the given conditions, we have: $31=a_1+(7-1)d$ or $31=a_1+6d$ 2. and $96=a_1+(20-1)d$ or $96=a_1+19d$ 3. Take the difference of the above two equations to get $13d=65$, thus $d=5$ 4. Find $a_1=31-6(5)=1$ 5. The general form is $a_n=1+5(n-1)=5n-4$,
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