Chapter 12: Q 47. (page 825)

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\sum_{n = 1}^{15} {(\frac{2}{3})}^{n}$

Short Answer

Expert verified

The sum of the given sequence is $1.9954$

Step by step solution

Step 1. Write the given information.

The given sequence is $\sum_{n = 1}^{15} {(\frac{2}{3})}^{n}$

Step 2. Find the common ratio.

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

Step 3. Find the sum.

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

$s_{15} = \frac{2}{3} \cdot \frac{1 - {\frac{2}{3}}^{15}}{1 - \frac{2}{3}} = \frac{2}{3} \cdot \frac{1 - {\frac{2}{3}}^{15}}{\frac{1}{3}} = 2 \cdot 1 - {\frac{2}{3}}^{15} = 1.9954$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\sum_{n = 1}^{15} {(\frac{2}{3})}^{n}$

Short Answer

Step by step solution

Step 1. Write the given 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

Decision Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.∑n=11523n

Short Answer

Step by step solution

Step 1. Write the given 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

Decision Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\sum_{n = 1}^{15} {(\frac{2}{3})}^{n}$