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If the sum to 2n terms of an Ap 2,5,8,11...

If the sum to 2n terms of an Ap 2,5,8,11 , `….` is equal to the sum to n terms of an AP 57,59,61,63, `….` , then n is equal to

A

10

B

11

C

12

D

13

Text Solution

Verified by Experts

The correct Answer is:
b
Let sum of 2n terms of an 2,5,8,11 ` ….."is" S_(2n)`
` S_(2n) = (2n)/2 [ 2xx2 +(2n-1)3] = n (4+6n-3)=n(6n+1)`
and sum of n terms of tha Ap 57, 59,61 ,63 `…. "is " S'_(n)`
` :. S'_(n) = n/2 [ 2 xx 57 +(n-1) 2] = n/2 (2n+112)`
According to the question, `S_(2n)=S'_(n)`
` rArr n(6n+1) =n/2 (2n+112)`
` rArr 12n +2 = 2n +112`
` rArr 10n = 110 `
` rArr n=11`
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