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: 27

Answer

An explicit rule for the sequence is $ a_n=17n-13$

Work Step by Step

The given recursive rule is $a_1=4,a_n=a_{n-1}+17$ First term is $a_1=4$. and common difference $d=17$. Explicit rule for an arithmetic sequence. $\Rightarrow a_n=a_1+(n-1)d$ Substitute $4$ for $a_1$ and $17$ for $d$. $\Rightarrow a_n=4+(n-1)17$ Use distributive property. $\Rightarrow a_n=4+17n-17$ Simplify. $\Rightarrow a_n=17n-13$
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