Chapter 12: Q 22. (page 824)

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given.
$a_{1} = 1, r = - \frac{1}{3}$

Short Answer

Expert verified

The $n t h$ term is $a_{n} = {\{\frac{- 1}{3}\}}^{n - 1}$ and the fifth term is $a_{5} = \frac{1}{81}$ .

Step by step solution

Step 1. Given information.

We have,

$a_{1} = 1$ and $r = - \frac{1}{3}$

The $n t h$ term of a geometric sequence is determined by formula $a_{n} = a_{1} r^{n - 1}$

Step 2. To find the fifth term and the nth term.

Substitute $a_{1} = 1, r = \frac{1}{3}$ and $n = 5$

$a_{n} = 1 {\{- \frac{1}{3}\}}^{n - 1} a_{n} = {\{- \frac{1}{3}\}}^{n - 1}$

and

$a_{5} = 1 {\{- \frac{1}{3}\}}^{5 - 1} a_{5} = 1 {\{- \frac{1}{3}\}}^{4} a_{5} = \frac{1}{81}$

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.

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given.
$a_{1} = 1, r = - \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the fifth term and the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Applied Mathematics

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the fifth term and the nth term of the geometric sequence whose initial term a1and common ratio rare given. a1=1,r=-13

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the fifth term and the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Applied Mathematics

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given.
$a_{1} = 1, r = - \frac{1}{3}$