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Chapter 12: Q 165. (page 1199)

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

鈭�i=194(2)i

Short Answer

Expert verified

The sum of geometric sequence is4,088.

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=194(2)i

Expand geometric sequence:

localid="1645458160215" 鈭�i=194(2)i=4(2)1+4(2)2+4(2)3+...+4(2)9=4(2)+4(4)+4(8)+...+4(512)=8+16+32+...+2048

02

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

First-term of geometric sequence is:

a1=8

Common ratio:

168=2,3216=2r=2

03

Step 3. Use the sum formula of geometric sequence. 

Sn=a1(1-rn)1-r

Substitute a1=8,r=2and n=9in the formula,

S9=8(1-29)1-2=8(1-29)-1=-8(1-29)=4,088

Therefore, the sum of geometric sequence is 4,088.

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