Chapter 12: Q 146. (page 1198)

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{13}$ given $a_{1} = 7$ and $r = 2$ .

Short Answer

Expert verified

The value of $a_{13}$ is $28, 672$ .

Step by step solution

Step 1. Write the given information and use the formula of general term

The given information is:

$a_{1} = 7$ and $r = 2$

The general term of a geometric sequence with the first term $a_{1}$ and the common ratio $r$ is:

$a_{n} = a_{1} r^{n - 1}$

Step 2. Substitute the given values into the formula

$a_{1} = 7, r = 2$ and $n = 13$
localid="1645273060798" $a_{13} = (7) {(2)}^{13 - 1} = (7) {(2)}^{12} = (7) (4096) = 28, 672$

$a_{13} = 28, 672$

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.

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{13}$ given $a_{1} = 7$ and $r = 2$ .

Short Answer

Step by step solution

Step 1. Write the given information and use the formula of general term

Step 2. Substitute the given values into the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Decision Maths

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.Finda13givena1=7andr=2.

Short Answer

Step by step solution

Step 1. Write the given information and use the formula of general term

Step 2. Substitute the given values into the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Decision Maths

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{13}$ given $a_{1} = 7$ and $r = 2$ .