Q4 of 85 Page 104

How many terms of A.P., 2, 7, 12, 17, ... add up to 990?

Formula used.


Sn = [2a + (n–1)d]


d = an + 1–an


⇒ S20 = 990


⇒ a = 2


⇒ d = an + 1–an


= 7 – 2 = 5


Sn = [2×2 + (n–1)5]


990 = [4 + 5n–5]


990 = [5n–1]


990×2 = 5n2–n


5n2–n–1980 = 0


n =


∴ n can be 20 or –19.8


Since, the number of terms cannot be negative


∴ Sum of 20 terms gives the sum of 990


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