Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-8 Geometric Sequences - Practice and Problem-Solving Exercises - Page 470: 22


The explicit formula is $a_{n}$=2 $\times$ (3$)^{n-1}$

Work Step by Step

You have to use the explicit formula The explicit formula is $a_{n}$=$a_{1}$ $\times$ (r$)^{n-1}$. The starting value is 2 so it is $a_{1}$. You have the sequence 2,6,18 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{6}{2}$=3 and r=$\frac{18}{6}$=3.So the common ratio is 3.Substitute the value of a1 and r into the explicit formula: The explicit formula is $a_{n}$=2 $\times$ (3$)^{n-1}$
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