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Question

In a G.P., T2+T5=216 and T4:T6=1:4 and all terms are integers, then its first term is:

A
16
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B
14
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C
12
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D
15
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Solution

The correct option is C 12
We know that nth term of an GP is given by arn1
Since, ar+ar4=216 and ar3ar5=14
r2=4r=2,2
When r=2, then 2a.(9)=216
a=12
When r=2, then 2a(18)=216
Thus, a=21614=1087, which is not an integer.
Therefore, a=12

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