Question

How many terms of the A.P. -6, $\frac{-12}{2}-\mathrm{5.....}$ Are needed to give the sum -25?

Answer 1

$-6,\frac{-12}{2}-5$…..

$a=-6$, $d=-11+6=-5$

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

$-25=\frac{n}{2}[-12+(n-1\left)\right(-5\left)\right]$

$=50=n[-7-5n]$.