Question

How many terms of series 54,51,48,....... Be taken so that their sum is 513? Explain the double answer.

Answer 1

Sn = n/2 ( 2a + (n-1)d)
513= n/2 (2* 54 +(n*-3) +3)
1026= 108n - 3n^2 +3n
3n^2 -111n +1026= 0
n^2 - 37n + 342 = 0
n= 18 or n = 19
the progression is towards negative side
therefore we get three answer