Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Review - Exercises - Page 890: 28

Answer

$a_{n}=6\times \left( \dfrac {5}{3}\right) ^{n-1}$

Work Step by Step

$a_{n}=a\times r^{n-1};a_{m}=a\times r^{m-1}$ $\dfrac {a_{n}}{a_{m}}=\dfrac {r^{n}}{r^{m}}=r^{n-m}$ $\dfrac {a_{5}}{a_{2}}=r^{5-2}=\dfrac {\left( \dfrac {1250}{27}\right) }{10}\Rightarrow \dfrac {125}{27}=r^{3}\Rightarrow r=\dfrac {5}{3}$ $\dfrac {a_{n}}{a_{2}}=\left( r\right) ^{n-2}=\dfrac {a_{n}}{10}=\left( \dfrac {5}{3}\right) ^{n-2}=\left( \dfrac {5}{3}\right) ^{n}\times \left( \dfrac {3}{5}\right) ^{2}\Rightarrow a_{n}=10\times \left( \dfrac {3}{5}\right) ^{2}\times \left( \dfrac {5}{3}\right) ^{n}=6\times \left( \dfrac {5}{3}\right) ^{n-1}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.