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Chapter 12: Q 163. (page 1199)

In the following exercises, find the sum of the geometric sequence.

鈭�i=115(2)i

Short Answer

Expert verified

The sum of geometric sequence is65,534.

Step by step solution

01

Step 1. Write the given information and then write out the first few terms.

The given information is:

鈭�i=115(2)i,

Expand geometric sequence:

鈭�i=115(2)i=(2)1+(2)2+(2)3+(2)4+...+(2)15=2+4+8+16+...+32,768

02

Step 2. Determine the first term and find common ratio.

First-term of geometric sequence is:

a1=2

Common ratio is:

42=2,84=2r=2

03

Step 3. Use the sum formula of geometric sequence.

Sn=a1(1-rn)1-r

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

S15=2(1-215)1-2=2(1-215)-1=-2(1-215)=65,534

Therefore, the sum of geometric sequence is65,534

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