Algebra 1

Published by Prentice Hall

Chapter 7 - Exponents and Exponential Functions - Concept Byte - Geometric Sequences - Page 453: 2

Answer

a) $\frac{1}{4}$ b) $\frac{5}{16}$, $\frac{5}{64}$, $\frac{5}{256}$

Work Step by Step

a) $\frac{1}{4}$ is the common ratio because each number in the sequence is $\frac{1}{4}$ of the number before it. In other words, each number in the sequence is being multiplied by $\frac{1}{4}$ (or divided by 4). As a result, this is the common ratio. b) To find the following numbers in the sequence, simply multiply the last number by $\frac{1}{4}$: $\frac{5}{4}$ x $\frac{1}{4}$ = $\frac{5}{16}$ $\frac{5}{16}$ x $\frac{1}{4}$ = $\frac{5}{64}$ $\frac{5}{64}$ x $\frac{1}{4}$ = $\frac{5}{256}$

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