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Question

The sum of first n terms of an G.P. is _____ when |r|<1.

A
Sn=a1(1rn)1r
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B
Sn=a1(1+rn)1r
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C
Sn=a1(1rn)1+r
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D
Sn=a1(1rn)r1
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Solution

The correct option is A Sn=a1(1rn)1r
A GP can be written as:
a,ar,ar2,ar3..............,arn1
sum=a+ar+ar2+ar3+.........+arn1
sum=a(rn1+rn2+rn3+rn4+...........+r+1)
We know that:
xn1x1=xn1+xn2+xn3+.............+x+1
Thus sum=a(rn1r1)

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