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Chapter 12: Q 157. (page 1199)

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

8,24,72,216,648,1944,...

Short Answer

Expert verified

The value ofS15is57,395,624.

Step by step solution

01

Step 1.  Write the given information, determine the first term and find common ratio.

The given sequence is:

8,24,72,216,648,1944,...

First term:

a1=8

Common ratio:

248=3,7224=3

r=3

02

Step 2. Use the sum formula of geometric sequence.

Sn=a1(1-rn)1-r

Substitute a1=8,r=3and n=15in the formula,

S15=8(1-315)1-3=8(1-315)-2=57,395,624

The sum of the first fifteen terms of geometric sequence is57,395,624.

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