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Chapter 12: Q 12.49 (page 1190)

Find the sum of the first 20terms of the geometric sequence3,6,12,24,48,96,鈥�.

Short Answer

Expert verified

The sum of the first 20terms is3220-1.

Step by step solution

01

Step 1. Given information

The geometric sequence is3,6,12,24,48,96,....

02

Step 2. Find the first and the common ratio.

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

Let a,rdenote the first term and the common ratio respectively.

a=3r=63=2

03

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

The sum of nterms of the sequence is given by Sn=a1-rn1-r.

Put a=3,r=2.

S20=31-2201-2=3220-1

=3145725

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