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

Answer

N/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