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Chapter 12: Q 158. (page 1199)

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

7,14,28,56,112,224,...

Short Answer

Expert verified

The value ofS15is229,369.

Step by step solution

01

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

The given sequence is:

7,14,28,56,112,224,...

First-term is:

a1=7

Common ratio:

147=2,2814=2r=2

02

Step 2. Use the sum formula of geometric sequence. 

Sn=a1(1-rn)1-r

Substitute a1=7,r=2and n=15in the formula,

Sn=7(1-215)1-2=7(1-215)-1=-7(1-215)=229,369

Therefore, the sum of the first fifteen terms of geometric sequence is229,369.

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