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Chapter 12: Q 160. (page 1199)

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

-4,12,-36,108,-324,972,...

Short Answer

Expert verified

The value ofS15is-14,348,908.

Step by step solution

01

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

The given sequence is:

-4,12,-36,108,-324,972,...

First-term is:

a1=-4

Common ratio:

12-4=-3,-3612=-3

r=-3

02

Step 2. Use the sum formula of geometric sequence.

Sn=a1(1-rn)1-r

Substitute a1=-4,r=-3and n=15in the formula,

S15=-4[1-(-3)15]1-(-3)=-4[1-(-3)15]4=-[1-(-3)15]=-14,348,908

Therefore, the sum of the first fifteen terms of the geometric sequence is-14,348,908.

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