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+r2−90=0 ⇒r4+10r2−9r2−90=0 ⇒(r2+10)(r2−9)=0 ⇒r2−9=0 ⇒r=±3