In a GP, fifth term is 4 times the third term, then the common ratio is ____.
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Let a be the first term and r be the common ratio of the G.P.
According to the given conditions,
S2=−4=a+ar...(1)
And a5=4×a3
⇒ar4=4ar2
⇒r2=4
∴r=±2
From (1) , we obtain −4=a(1+r)
⇒a=−1+r4
For r=−2,a=4 and for r=2,a=−34
Thus , the required G.P. is 3−4,3−8,3−16... or 4, −8, 16, −32, 64....
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