Chapter 12: Q 12.50 (page 1190)

Find the sum of the first $20$ terms of the geometric sequence $6, 18, 54, 162, 486, 1, 458, \dots$

Short Answer

Expert verified

Sum of the first $20$ terms of the geometric sequence is $\begin{array}{rcl} - 3 (1 - 3^{20}) \end{array}$ .

Step by step solution

Step 1. Given information

The geometric sequence is $6, 18, 54, 162, 486, 1, 458, . . .$

Step 2. Find the first term and the common ratio.

Consider the geometric sequence $6, 18, 54, 162, 486, 1, 458, . . .$

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

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

Step 3. Find the sum of the first 20 terms of the geometric sequence.

Put $a = 6, r = 3, n = 20$ in $S_{n} = \frac{a (1 - r^{n})}{1 - r}$

$\begin{array}{rcl} S_{20} & = & \frac{6 (1 - 3^{20})}{1 - 3} \\ = & - 3 (1 - 3^{20}) \end{array}$

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Find the sum of the first $20$ terms of the geometric sequence $6, 18, 54, 162, 486, 1, 458, \dots$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first term and the common ratio.

Step 3. Find the sum of the first 20 terms of the geometric sequence.

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Find the sum of the first 20terms of the geometric sequence6,18,54,162,486,1,458,…

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first term and the common ratio.

Step 3. Find the sum of the first 20 terms of the geometric sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the sum of the first $20$ terms of the geometric sequence $6, 18, 54, 162, 486, 1, 458, \dots$