Chapter 12: Q 44. (page 825)

In Problems 39– 44, find each sum.
$2 + \frac{6}{5} + \frac{18}{25} + . . . + 2 {(\frac{3}{5})}^{n - 1}$

Short Answer

Expert verified

The sum of the given sequence is $5 \cdot 1 - {\frac{3}{5}}^{n}$

Step by step solution

Step 1. Write the information.

The given sequence is $2 + \frac{6}{5} + \frac{18}{25} + . . . + 2 {(\frac{3}{5})}^{n - 1}$

Step 2. Find the common ratio.

$a_{1} = 2, a_{2} = \frac{6}{5}, a_{3} = \frac{18}{25} \frac{a_{2}}{a_{1}} = \frac{\frac{6}{5}}{2} = \frac{3}{5} \frac{a_{3}}{a_{2}} = \frac{\frac{18}{25}}{\frac{6}{5}} = \frac{3}{5} r = \frac{3}{5}$

Step 3. Find the sum

The formula for the sum of nth term is $s_{n} = \frac{a_{1} (1 - r^{n})}{1 - r}$

$s_{n} = 2 \cdot \frac{1 - {\frac{3}{5}}^{n}}{1 - \frac{3}{5}} = 2 \cdot \frac{1 - {\frac{3}{5}}^{n}}{\frac{2}{5}} = 5 \cdot 1 - {\frac{3}{5}}^{n}$

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In Problems 39– 44, find each sum.
$2 + \frac{6}{5} + \frac{18}{25} + . . . + 2 {(\frac{3}{5})}^{n - 1}$

Short Answer

Step by step solution

Step 1. Write the information.

Step 2. Find the common ratio.

Step 3. Find the sum

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In Problems 39– 44, find each sum.2+65+1825+...+235n-1

Short Answer

Step by step solution

Step 1. Write the information.

Step 2. Find the common ratio.

Step 3. Find the sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Pure Maths

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Study anywhere. Anytime. Across all devices.

In Problems 39– 44, find each sum.
$2 + \frac{6}{5} + \frac{18}{25} + . . . + 2 {(\frac{3}{5})}^{n - 1}$