Explanation:

As given in problem, A=100, D=-5 

Sum of AP = n/2 [2a+(n-1)d]

975 = n/2 [200+(n-1)-5] 

1950 = n(200-5n+5) 

1950 = 205n-5n^2 

5n^2-205n+1950 = 0 

n^2-41n+391 = 0 

n^2-26n-15n+390 = 0 

n(n-26) - 15(n-26) = 0 

n = 15 or 26.  

n = 15 months.

Hence, option 2 is the correct answer.