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Chapter 12: Q 164. (page 1199)

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

鈭�i=110(3)i

Short Answer

Expert verified

The sum of geometric sequence is88,572

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=110(3)i

Expand the geometric sequence:

localid="1645457149258" 鈭�i=110(3)i=(3)1+(3)2+(3)3+...+(3)10=3+9+27+...+59049

02

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

First-term of geometric sequence is:

a1=3

Common ratio:

93=3,279=3r=3

03

Step 3. Use the sum formula of geometric sequence. 

Sn=a1(1-rn)1-r

Substitute a1=3,r=3and n=10in the formula,

S10=3(1-315)1-3=3(1-315)-2=-1.5(1-315)=88,572

Therefore, the sum of geometric sequence is88,572.

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