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Question

The first term of a G.P. is 1. If the sum of the third and fifth terms of the G.P. is 90, then the common ratio of the G.P. is

A
±5
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B
±2
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C
±3
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D
±4
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Solution

The correct option is C ±3
Let r be the common ratio of the G.P. It is given that the first term is a=1. Now,
a3+a5=90
ar2+ar4=90
r2+r4=90
r4+r290=0
r4+10r29r290=0
(r2+10)(r29)=0
r29=0
r=±3

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