Chapter 12: Q. 3 (page 838)

In Problems 1– 4, write down the first five terms of each sequence.
$a_{1} = 3, a_{n} = \frac{2}{3} a_{n - 1}$

Short Answer

Expert verified

The first five terms of the sequence are: $3, 2, \frac{4}{3}, \frac{8}{9}, \frac{16}{27}$ .

Step by step solution

Step 1. Given information.

General term of the sequence:

$a_{n} = \frac{2}{3} a_{n - 1}$

First term of the sequence:

$a_{1} = 3$

Step 2. Substitute first four integral value of n starting from 2 in the expression anand solve.

Second term:

$a_{2} = \frac{2}{3} a_{2 - 1} = \frac{2}{3} a_{1} = \frac{2}{3} . 3 = 2$

Third term:

$a_{3} = \frac{2}{3} a_{3 - 1} = \frac{2}{3} a_{2} = \frac{2}{3} . 2 = \frac{4}{3}$

Fourth term:

$a_{4} = \frac{2}{3} a_{4 - 1} = \frac{2}{3} a_{3} = \frac{2}{3} . \frac{4}{3} = \frac{8}{9}$

Fifth term:

$a_{5} = \frac{2}{3} a_{5 - 1} = \frac{2}{3} a_{4} = \frac{2}{3} . \frac{8}{9} = \frac{16}{27}$

First five terms : $3, 2, \frac{4}{3}, \frac{8}{9}, \frac{16}{27}$

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In Problems 1– 4, write down the first five terms of each sequence.
$a_{1} = 3, a_{n} = \frac{2}{3} a_{n - 1}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute first four integral value of n starting from 2 in the expression anand solve.

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In Problems 1– 4, write down the first five terms of each sequence. a1=3,an=23an-1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute first four integral value of n starting from 2 in the expression anand solve.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 1– 4, write down the first five terms of each sequence.
$a_{1} = 3, a_{n} = \frac{2}{3} a_{n - 1}$