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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 38. (page 825)

In Problems 31鈥�38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{3} = \frac{1}{3}, a_{6} = \frac{1}{81}$

Short Answer

Expert verified

The common ratio is $r = \frac{1}{3}$ and $a_{n} = 3 路 {\frac{1}{3}}^{n - 1}$

Step by step solution

01

Step 1. Write the given information.

Given that $a_{3} = \frac{1}{3}; a_{6} = \frac{1}{81}$

02

Step 2. Find the common ratio and nth term.

The formula is

$a_{n} = a_{1} 路 r^{3 - 1} a_{3} = a_{1} 路 r^{2} \frac{1}{3} = a_{1} 路 r^{2} a_{6} = a_{1} 路 r^{6 - 1} \frac{1}{81} = a_{1} 路 r^{5} \frac{\frac{1}{3}}{\frac{1}{81}} = \frac{a_{1} 路 r^{2}}{a_{1} 路 r^{5}} 27 = \frac{1}{r^{3}} r = \frac{1}{3} a_{1} = 3 a_{n} = 3 路 {\frac{1}{3}}^{n - 1}$

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Most popular questions from this chapter

How much do you need to invest now at $5 %$ per annum compounded monthly so that in 1 year you will have $$ 10000$ ?

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