# 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 90th term making the sum 900 again.

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