Chapter 12: Q 34. (page 825)

In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

Short Answer

Expert verified

The common ratio is $r = \frac{1}{4}$ and the nth term is $4 \cdot {\frac{1}{4}}^{n - 1}$

Step by step solution

Step 1. Write the given information.

The geometric sequence is $4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

Step 2. Find the common ratio.

$a_{1} = 4, a_{2} = 1, a_{3} = \frac{1}{4} \frac{a_{2}}{a_{1}} = \frac{1}{4} \frac{a_{3}}{a_{2}} = \frac{\frac{1}{4}}{1} = \frac{1}{4} r = \frac{1}{4}$

Step 3. Find the nth term.

The formula for the nth term is $a_{n} = a_{1} \cdot r^{n - 1}$

$a_{n} = 4 \cdot {\frac{1}{4}}^{n - 1}$

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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.
$4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio.

Step 3. Find the 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.4,1,14,116,...

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio.

Step 3. Find the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

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.
$4, 1, \frac{1}{4}, \frac{1}{16}, . . .$