How many terms of the A.P -15, -11, -7, ....... are needed to make the sum 744 ?

How many terms of the A.P -15, -11, -7, ....... are needed to make the

1.	How many terms of the A.P -15, -11, -7, ....... are needed to make the sum 744 ?
Answer» a=-15, d=-11+15=4 , Sn=744Sn=n/2{2a+(n-1)d} , n/2{-30+(n-1)4}=744 ,n/2(-30+4n-4)=744 ,n(-34+4n)=1488 ,4n^2-34n-1488=0 ,2n^2-17n-744=0 ,2n^2-48n+31n-744=0 ,2n(n-24)+31(n-24)=0 ,(n-24)(2n+31)=0. ,n=24 or n=-31/2(which is not possible). Hence,n=24 24 terms.