College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 29

Answer

$a_n=2^n$

Work Step by Step

RECALL: The nth term of a geometric sequence is given by the formula: $a_n=a_1(r^{n-1})$ where $r$ = common ratio $a_1$ = first term $a_n$ = nth term Notice that each term is twice the term before it. This means that the sequence is geometric and that the common ratio is $2$. The first term is $2$ so $a_1=2$. Therefore the nth term of the sequence can be found using the formula: $a_n=2(2^{n-1}) \\a_n=2^{n-1+1} \\a_n=2^n$
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