College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises - Page 617: 104

Answer

Geometric sequence with common ratio $10^d$

Work Step by Step

We are given the arithmetic sequence: $$a_1,a_2,a_3,\dots$$ where $a_{k+1}-a_k=d$. Consider the sequence: $$10^{a_1},10^{a_2},10^{a_3}\dots$$ We calculate the ratio of two consecutive terms: $$\dfrac{10^{a_{k+1}}}{10^{a_k}}=10^{a_{k+1}-a_k}=10^d.$$ So the second sequence is geometric, its common ratio being $10^d$.
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