College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises: 19

Answer

geometric sequence $\frac{1}{t}$

Work Step by Step

We are given: $t^{3}, t^{2}, t, 1$, ... We can see that this is a geometric sequence by dividing the terms: $\displaystyle \frac{a_2}{a_1}=\frac{t^2}{t^3}=\frac{1}{t}$ $\displaystyle \frac{a_3}{a_2}=\frac{t}{t^2}=\frac{1}{t}$ $\displaystyle \frac{a_4}{a_3}=\frac{1}{t}$ Thus $r=\frac{1}{t}$. So the 5th term is: $a_{5}=a_{4}*r=1*\frac{1}{t}=\frac{1}{t}$
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