Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 6 - Exponential Functions and Sequences - 6.7 - Recursively Defined Sequences - Exercises - Page 345: 28

Answer

An explicit rule for the sequence is $a_n=5(-5)^{n-1}$

Work Step by Step

The given recursive rule is $a_1=5,a_n=-5a_{n-1}$ First term is $a_1=5$. and common ratio $r=-5$. Explicit rule for an geometric sequence. $\Rightarrow a_n=a_1r^{n-1}$ Substitute $5$ for $a_1$ and $-5$ for $r$. $\Rightarrow a_n=5(-5)^{n-1}$
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