Question

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

Answer 1

first term $a=-6$

Common Difference $d=\frac{1}{2}$

Sum $=-25$

$\frac{n}{2}(2a+(n-1\left)d\right)=-25$

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

$⟹n^2-25n+100=0$

$⟹n=5,20$