Chapter 12: Q 38. (page 825)

In Problems 31–38, 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 $a_{n} = 3 \cdot {\frac{1}{3}}^{n - 1}$

Step by step solution

Step 1. Write the given information.

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

Step 2. Find the common ratio and nth term.

The formula is

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

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In Problems 31–38, 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

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio and nth term.

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In Problems 31–38, find the nth term anof each geometric sequence. When given, r is the common ratio.a3=13,a6=181

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio and nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Applied Mathematics

Discrete Mathematics

Geometry

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Study anywhere. Anytime. Across all devices.

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