Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set: 7

Answer

$48, 24, 12, 6, 3$

Work Step by Step

The general term $a_n$ of a geometric sequence is given by $a_n = a_1r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio. We plug in $n = 1, 2, 3, 4, 5$ to find the first five terms of the geometric sequence $a_1 = 48\cdot\frac{1}{2}^{1-1} = 48\cdot\frac{1}{2}^0=48\cdot1=48$ $a_2 = 48\cdot\frac{1}{2}^{2-1} = 48\cdot\frac{1}{2}^1=48\cdot\frac{1}{2}=24$ $a_3 = 48\cdot\frac{1}{2}^{3-1} = 48\cdot\frac{1}{2}^2=48\cdot\frac{1}{4}=12$ $a_4 = 48\cdot\frac{1}{2}^{4-1} = 48\cdot\frac{1}{2}^3=48\cdot\frac{1}{8}=6$ $a_5 = 48\cdot\frac{1}{2}^{5-1} = 48\cdot\frac{1}{2}^4=48\cdot\frac{1}{16}=3$
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