Chapter 12: Q 143. (page 1198)

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.
$a_{1} = 27$ and $r = \frac{1}{3}$

Short Answer

Expert verified

The first five terms of the geometric sequence are $27, 9, 3, 1, \frac{1}{3}$ .

Step by step solution

Step 1. Write the given information and find the second term with the help of the first term and common ratio.

The given information is:

First term $(a_{1}) = 27$

Common ratio:

$(r) = \frac{1}{3}$

Second term:

$a_{2} = a_{1} r = 27 \times \frac{1}{3} = 9$

The second term of the sequence is $9$ .

Step 2. Find the next three terms in the same manner.

Third term:

$a_{3} = a_{2} r = 9 \times \frac{1}{3} = 3$

The third term of the sequence is $3$ .

Fourth term:

$a_{4} = a_{3} r = 3 \times \frac{1}{3} = 1$

The fourth term of the sequence is $1$ .

Fifth term:

$a_{5} = a_{4} r = 1 \times \frac{1}{3} = \frac{1}{3}$

The fifth term of the sequence is $\frac{1}{3}$ .

Step 3. Write the first five terms of the sequence.

The first five terms of the sequence are:

$27, 9, 3, 1, \frac{1}{3}$ .

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, write the first five terms of each geometric sequence with the given first term and common ratio.
$a_{1} = 27$ and $r = \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Write the given information and find the second term with the help of the first term and common ratio.

Step 2. Find the next three terms in the same manner.

Step 3. Write the first five terms of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.a1=27andr=13

Short Answer

Step by step solution

Step 1. Write the given information and find the second term with the help of the first term and common ratio.

Step 2. Find the next three terms in the same manner.

Step 3. Write the first five terms of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.
$a_{1} = 27$ and $r = \frac{1}{3}$