Chapter 12: Q 12.49 (page 1190)

Find the sum of the first $20$ terms of the geometric sequence $3, 6, 12, 24, 48, 96, \dots$ .

Short Answer

Expert verified

The sum of the first $20$ terms is $\begin{array}{rcl} 3 (2^{20} - 1) \end{array}$ .

Step by step solution

Step 1. Given information

The geometric sequence is $3, 6, 12, 24, 48, 96, . . .$ .

Step 2. Find the first and the common ratio.

Consider the sequence $3, 6, 12, 24, 48, 96, . . .$

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

$\begin{array}{rcl} a & = & 3 \\ r & = & \frac{6}{3} \\ = & 2 \end{array}$

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

The sum of $n$ terms of the sequence is given by $S_{n} = \frac{a (1 - r^{n})}{1 - r}$ .

Put $a = 3, r = 2$ .

$\begin{array}{rcl} S_{20} & = & \frac{3 (1 - 2^{20})}{1 - 2} \\ = & 3 (2^{20} - 1) \end{array}$

$= 3145725$

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Find the sum of the first $20$ terms of the geometric sequence $3, 6, 12, 24, 48, 96, \dots$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first 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 sequence3,6,12,24,48,96,….

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the first 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

Probability and Statistics

Applied Mathematics

Decision Maths

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find the sum of the first $20$ terms of the geometric sequence $3, 6, 12, 24, 48, 96, \dots$ .