How many terms of the A.P. `-6,-(11)/(2),-5…` are needed to give the sum -25?

Options

A. `5,20`
B. `5,10`
C. `6,12`
D. `6,10`

Answer

`A`

Explanation

Let the sum of n terms be -25.
`"First term "a_(1)=-6,`
`"Common difference "d=a_(2)-a_(1)=-(11)/(2)-(-6)=(1)/(2)`
`therefore" Sum of n terms"`
`=(n)/(2)[2a+(n-1)d]=(n)/(2)[2xx(-6)+(n-1)xx(1)/(2)]`
`=(n)/(2)[-12+(n-1)/(2)]=(n)/(2)xx(n-25)/(2)=(n^(2)-25n)/(4)`
`therefore" "(n^(2)-25n)/(4)=-25`
`rArr" "n^(2)-25n+100=0`
`rArr" "n^(2)-5n-20n+100=0`
`rArr" "n(n-5)-20(n-5)=0`
`rArr" "(n-5)(n-20)=0`
`rArr" "n=5 or 20`
Therefore, no. of terms = 5 or 20