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 4 - Writing Linear Functions - 4.6 - Arithmetic Sequences - Monitoring Progress - Page 212: 8


An equation for the $n^{th}$ term is $a_n=n+3$ and $a_{25}=28$

Work Step by Step

The given arithmetic sequence is $4,5,6,7,...$ The first term $a_1=4,$ and the common difference is $d=5-4=1$ The $n^{th}$ term formula is $\Rightarrow a_n=a_1+(n-1)d$ Substitute $4$ for $a_1$ and $1$ for $d$. $\Rightarrow a_n=4+(n-1)1$ Simplify. $\Rightarrow a_n=4+n-1$ $\Rightarrow a_n=n+3$ Substitute $25$ for $n$. $\Rightarrow a_{25}=25+3$ Simplify. $\Rightarrow a_{25}=28$.
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