Chapter 12: Q 7. (page 824)

Show that each sequence is geometric. Then find the common ratio and write out the first four terms $\{s_{n}\} = \{3^{n}\}$ .

Short Answer

Expert verified

The common ratio is $3$ and the first four terms are $3, 9, 27, 81$ .

Step by step solution

Step 1. Given information.

We have given sequence $\{s_{n}\} = \{3^{n}\}$ .

The nth term and $(n - 1)$ th term are $s_{n} = 3^{n} s_{n - 1} = 3^{n - 1}$

Step 2. To find the common ratio.

We have,

$r = \frac{s_{n}}{s_{n - 1}} r = \frac{3^{n}}{3^{n - 1}} r = 3^{n - n + 1} r = 3$

Since the ratio of the successive term is the non zero constant $3$ , therefore $\{s_{n}\}$ is a geometric sequence with common ratio is $3$ .

Step 3. To find the terms.

We have

\{s_{n}\} = 3^{n} s_{1} = 3^{1} s_{1} = 3 s_{2} = 3^{2} s_{2} = 9 s_{3} = 3^{3} s_{3} = 27

and

s_{4} = 3^{4} s_{4} = 81

Thus, the first four terms are $3, 9, 27, 81$ .

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.

Show that each sequence is geometric. Then find the common ratio and write out the first four terms $\{s_{n}\} = \{3^{n}\}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the common ratio.

Step 3. To find the terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Discrete Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Show that each sequence is geometric. Then find the common ratio and write out the first four termssn=3n.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the common ratio.

Step 3. To find the terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Discrete Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Show that each sequence is geometric. Then find the common ratio and write out the first four terms $\{s_{n}\} = \{3^{n}\}$ .