Answer
$x=2$
Work Step by Step
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{a_3}{a_2}=\frac{a_2}{a_1}\\\frac{x+2}{x}=\frac{x}{x-1}\\(x+2)(x-1)=x^2\\x^2+x-2=x^2\\x-2=0\\x=2$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 825: 84
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