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Question
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
Solution
A.P. = 27, 24, 21,…
a = 27
d = 24 – 27 = -3
Sn =0
Let n terms be there in A.P.
Sn = `n/(2)[2a + (n -1)d]`
⇒ 0 = `n/(2)[(2 xx 27) + (n - 1)(-3)]`
⇒ 0 = n[54 – 3n + 3]
⇒ n[57 –3n] = 0
⇒ (57 – 3n) = `(0)/n` = 0
⇒ 3n = 57
∴ n = `(57)/(3)`
= 19.
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