Question

How many terms of the A.P -6,$-\frac{11}{2},-5$.......are needed to give the sum -25?

Answer 1

Given,

$a=-6$

$d=-\frac{11}{2}-(-6)=\frac{1}{2}$

Formula,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$-25=\frac{n}{2}\left[2\right(-6)+(n-1\left)\frac{1}{2}\right]$

$-50=n\left[\frac{-24+n-1}{2}\right]$

$n^2-25n+100=0$

$(n-20)(n-5)=0$

$\therefore n=5,20$

Therefore the number of terms required is $5$ or $20$