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Question

If (5+9+13+.n)(7+9+11+..12)=512 , then n equals


A

5

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B

6

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C

9

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D

12

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Solution

The correct option is B

6


Explanation for correct option:

Let S1=5+9+13+.n terms

Here the first term a=5 and common difference is 4

Now,

S1=n22a+(n-1)d

=n210+(n-1)4

=n2(6+4n)=3n+2n2

S2=7+9+11+12terms

=122(14+11×2)=6(14+22)=216

Divide S1 by S2, we get

S1S2=512

(3n+2n2)216=512

2n2+3n-90=0

(2n+15)(n-6)=0

n=-152 or n=6

The number of terms can not be negative so the answer is n=6 .

Hence, the option (B) is correct .


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