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Chapter 12: Q. 292 (page 1219)

In the following exercises, find the sum of the first fifteen terms of each geometric sequence.

3,12,48,192,768,3072...

Short Answer

Expert verified

The sum of first fifteen terms of geometric sequence is1073741823

Step by step solution

01

Step 1. Given information

The given G.P. is3,12,48,192,768,3072...

02

Step 2. The sum of first n terms of the geometric sequence.

Sn=a1(1-rn)1-r

03

Step 3. The sum of the first fifteen terms of geometric sequence.

a1=3r=123r=4n=15

Now sum is

S15=3(1-415)1-4S15=3(1-415)-3S15=(415-1)S15=1073741823

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