College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding: 16

Answer

Th sequence is geometric with a common ratio of $9$. The first four terms are: $f_1=9$ $f_2=81$ $f_3=729$ $f_4=6561$

Work Step by Step

Substitute $1, 2, 3,$ and $4$ for $n$ into the given formula: $f_1=3^{2\cdot 1}=3^2 = 9$ $f_2=3^{2\cdot 2 }=3^4 = 81$ $f_3=3^{2\cdot 3}=3^6 = 729$ $f_4=3^{2\cdot 4}=3^8 = 6561$ To check if the sequence is geometric, find the ratio of each successive pairs: $\dfrac{a_2}{a_1}=\dfrac{81}{9}=9$ $\dfrac{a_3}{a_2}=\dfrac{729}{81}=9$ $\dfrac{a_4}{a_3}=\dfrac{6561}{729}=9$ The common ratios are the same, so the sequence is geometric with a common ratio of $9$.
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