Question

how many terms of the ap .24+21+18+15+...be taken continuously so that their sum is -351?

Answer 1

In Given AP.  a = 24
              and, d = 21 - 24 = -3

 We have to find n for Sn = -351

          so, n/2[2(a) + (n-1)d] = -351
             so, n[2*24 + (n-1)-3] = -702
              
             = n(48 + 3-3n) = -702
             = n(51-3n) = -702
                51n - 3n^2 = -702
 On Dividing whole Eqn by 3
                17n - n^2 = -234
              So, n^2 - 17n - 234 = 0
                     n^2 -26n + 9n -234 = 0
                  n(n-26)  +9(n-26) = 0

      so , n= 26,-9
But n can't be negative 

So, 26 terms should be taken to get the required sum.