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 344: 16

Answer

A recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+8$

Work Step by Step

The given sequence from the table is $3,11,19,27,35,...$ The first term is $a_1=3$. Calculate difference between each pair of consecutive terms. $11-3=8$ $19-11=8$ $27-19=8$ $35-27=8$ The common difference is $d=8$. So, the sequence is arithmetic. Recursive equation for an arithmetic sequence. $a_n=a_{n-1}+d$ Substitute $8$ for $d$. $a_n=a_{n-1}+8$ Hence, a recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+8$
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