Question

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

Answer 1

$\begin{array}{c}Sn=-25\\ A.P=-6,-\frac{11}{2},-5\\ firstterm=-6\\ commondifference=-\frac{11}{2}+6=\frac{1}{2}\\ Thenweknow\\ Sn=\frac{n}{2}\left[2a+(n-1)d\right]\\ -25=\frac{n}{2}\left[-12+(n-1)\frac{1}{2}\right]\\ -50=-12n+\frac{n^2}{2}-\frac{n}{2}\\ \Rightarrow -2\times 50=-25n+n^2\\ -100=h^2-25n\\ h^2-25n+100=0\\ \left[\because n=20issatisfytheequationwetakenumbertermis20\right]\\ n^2-20n-5n+100=0\\ n(n-20)-5(n-20)=0\\ (n-5)(n-20)=0\\ n=5orn=20\\ \therefore n=20\end{array}$