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If a(1),a(2)a(3),….,a(15) are in A.P and...

If `a_(1),a_(2)a_(3),….,a_(15)` are in `A.P` and `a_(1)+a_(8)+a_(15)=15`, then `a_(2)+a_(3)+a_(8)+a_(13)+a_(14)` is equal to

A

`25`

B

`35`

C

`10`

D

`15`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Given `A.P.` is `a_(1),a_(2),a_(3),…….,a_(15)`
`a_(1)+a_(15)=a_(2)+a_(14)=….=2a_(8)`
`a_(1)+a_(15)+a_(8)=(3)/(2)(a_(1)+a_(15))=15`
`impliesa_(1)+a_(15)=10`
`a_(2)+a_(3)+a_(8)+a_(13)+a_(14)=2(a_(1)+a_(15))+a_(8)`
`=2(10)+5=25`
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