Question

Which term of the AP 25, 20, 15, ... is the first negative term?
(a) 9th
(b) 8th
(c) 7th
(d) 10th

Answer 1

(c) 7^th
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Here, a = 25 and d = (20 - 25) = - 5
Let the n^th term of the given AP be the first negative term.
Then T_{n <} 0
⇒ a + (n -1) d < 0
⇒ 25 + (n - 1) ⨯ (-5) < 0
⇒ 30 - 5n < 0
⇒ 30 < 5n
⇒ 5n > 30
⇒ n > 6
∴ n = 7

Hence, the 7^th term is the first negative term.