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: 20

Answer

The sequence is geometric. The common ratio is $e^2$.

Work Step by Step

A geometric sequence has a common ratio $r$. The common ratio is multiplied to the current term to get the next term of the sequence. The common ratio is equal to the the quotient of a term and the term before it. Solve for the ratio of each pair of consecutive terms. USe the rule $\dfrac{a^m}{a^n} = a^{m-n}$ to obtain: $\dfrac{e^4}{e^2} = e^{4-2} = e^2 \\\dfrac{e^6}{e^4}=e^{6-4} = e^2 \\\dfrac{e^8}{e^6} =e^{8-6} = e^2$ The consecutive terms have a common ratio so the sequence is geometric. The common ratio is $e^2$.
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