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Chapter 12: Q 159. (page 1199)

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

-6,12,-24,48,-96,192,...

Short Answer

Expert verified

The value ofS15is-65,538.

Step by step solution

01

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

The given sequence is:

-6,12,-24,48,-96,192,...

First-term is:

a1=-6

Common ratio:

12-6=-2,-2412=-2r=-2

02

Step 2. Use the sum formula of geometric sequence.

Sn=a1(1-rn)1-r

Substitute a1=-6,r=-2and n=15in the formula,

S15=-6[1-(-2)15]1-(-2)=-6[1-(-2)15]1+2=-6[1-(-2)15]3=-65,538

The sum of the first fifteen terms of the geometric sequence is-65,538.

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