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Question

If the third term of a G.P. is 12 and its sixth term is 96, find the sum of 9 terms.

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Solution

Given that: T3=12 and T6=96
T3=12
ar2=12 ......... (1)
T6=96
ar5=96 ........ (2)
divide (2) by (1): ar5ar2=9612r3=8
r3=23
r=2
Consider, ar2=12
a(2)2=12a×4=12a=3
Now, let us find S9.
Sn=a(rn1)r1
S9=3(291)21=3(5121)1=3(511)
S9=1533

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