Chapter 12: Q 12.47 (page 1189)

Find the ninth term of the sequence $6, 18, 54, 162, 486, 1, 458, \dots$ .Then find the general term for the sequence.

Short Answer

Expert verified

The ninth term is and the general term are equal to $39366, 6 {(3)}^{n - 1}$ respectively.

Step by step solution

Step 1. Given information

Sequence is $6, 18, 54, 162, 486, 1, 458, . . .$

Step 2. Find the ninth term of the sequence.

Consider the sequence:

$6, 18, 54, 162, 486, 1, 458, . . .$

Let $a, r$ denote the first term and the common ratio respectively.

$\begin{array}{rcl} a & = & 6 \\ r & = & \frac{18}{6} \\ = & 3 \end{array}$

$\begin{array}{rcl} a_{n} & = & a r^{n - 1} \\ a_{9} & = & 6 {(3)}^{9 - 1} \\ = & 6 (3^{8}) \\ = & 39366 \end{array}$

Step 3, Find the general term of the sequence.

Put $a = 6, r = 3$ in the formula $a_{n} = a r^{n - 1}$ .

So,

$a_{n} = 6 {(3)}^{n - 1}$

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Find the ninth term of the sequence $6, 18, 54, 162, 486, 1, 458, \dots$ .Then find the general term for the sequence.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the ninth term of the sequence.

Step 3, Find the general term of the sequence.

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Find the ninth term of the sequence 6,18,54,162,486,1,458,….Then find the general term for the sequence.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the ninth term of the sequence.

Step 3, Find the general term of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Calculus

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the ninth term of the sequence $6, 18, 54, 162, 486, 1, 458, \dots$ .Then find the general term for the sequence.