Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 9 - Sequences and Series - 9-2 Arithmetic Sequences - Practice and Problem-Solving Exercises - Page 576: 42


Recursive formula: $a_{1}=0$ ,$a_{n}=a_{n-1}+6$ Explicit formula:$a_{n}=6(n-1)$

Work Step by Step

The sequence is $0,6,12,18,24$. The first term is $0$ and the common difference is $6$. $\text{Explicit formula}$: The explicit formula is $a_{n}=a_{1}+(n-1)d$ where $a_1$=first term and $d$=common difference. Substitute the values of the common difference and the first term to obtain: $a_{n}=a_{1}+(n-1)d$ $a_{n}=0+(n-1)6$ $a_{n}=6(n-1)$ $\text{Recursive formula}$: The recursive formula is $a_{n}$=$a_{n-1}+d$. Substitute the value of $d$ to obtain: $a_{n}=a_{n-1}+6$, where $a_1=0$
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