Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.3 - Geometric Sequences - 12.3 Exercises - Page 864: 5

Answer

a. 7, 21, 63, 189, 567 b. r = 3 c. see below
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Work Step by Step

A geometric sequence is a sequence whose terms are obtained by multiplying each term by the same fixed constant $r$ to get the next term. A geometric sequence has the form $a, ar, ar^{2}, ar^{3}, \ldots$ The number $a$ is the first term of the sequence, and the number $r $is the common ratio. The nth term of the sequence is $\quad a_{n}=ar^{n-1}$ -------------- By comparing the general formula for the n-th term, $a=7, r=3.$ a. The first five terms $a_{1}=7$ $a_{2}=7(3)=21$ $a_{3}=21(3)=63$ $a_{4}=63(3)=189$ $a_{5}=189(3)=567$ b. $r=3$ c. graphed in desmos.com (image attached in answer)
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