How many terms of the arithmetic sequence 99, 97, 98, … must be added to get 900?

sum of an AP =

In this question we need to find n and a = 99, d = –2

we’ll put the values in the above equation.

⇒ n[198 – 2n + 2] = 1800

⇒ 2n² – 200n + 1800 = 0

⇒ n² – 100n + 900 = 0

⇒ n² – 10n – 90n + 900 = 0

⇒ n(n–10) – 90(n–10) = 0

⇒ (n–90)(n–10) = 0

⇒ n = 90,10

If we take 10 then after ten terms its sum would become 900.

If we take 90, then after 10 terms its sum would be 900 and then it will increase until a certain point and then again the sum will start decreasing because of negative values which will continue till 90^th term making the sum 900 again.