Question

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`

Answer 1

Correct Answer - 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`