Q. 34.5( 2 Votes )

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

Answer :

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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