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Chapter 12: Q 162. (page 1199)

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

256,64,16,4,1,14,116,...

Short Answer

Expert verified

The value ofS15is鈮�341.3.

Step by step solution

01

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

The given sequence is:

256,64,16,4,1,14,116,...

First-term is:

a1=256

Common ratio:

64256=14,1664=14r=14

02

Step 2. Use the sum formula of geometric sequence. 

Sn=a1(1-rn)1-r

Substitute a1=256,r=14and n=15in the formula,

role="math" localid="1645371117507" S15=256[1-(14)15]1-14=256[1-(14)15]34鈮�341.3

The sum of the first fifteen terms of the geometric sequence is鈮�341.3.

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