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Question

# In an increasing geometric series, the sum of the second and the sixth term is 252 and the product of the third and fifth term is 25. Then, the sum of 4th,6th and 8th terms is equal to :

A
35
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B
30
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C
26
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D
32
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Solution

## The correct option is A 35Let a be the first term and r be the common ratio. ar+ar5=252 and ar2×ar4=25 ⇒a2r6=25 ⇒ar3=5 ⇒a=5r3 …(1) Now, 5rr3+5r5r3=252 [From (1)] ⇒1r2+r2=52 Put r2=t ⇒t2+1t=52 ⇒2t2−5t+2=0 ⇒(2t−1)(t−2)=0 ⇒t=12,2 ⇒r2=12,2 ⇒r=√2 as the G.P. is increasing. ∴ar3+ar5+ar7 =ar3(1+r2+r4) =5(1+2+4)=35

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