Question

Which term of the AP 20, 17, 14, ... is the first negative term?
(a) 6th
(b) 7th
(c) 8th
(d) 9th

Answer 1

( c) 8^th

Here, a = 20 and d = (17 − 20) = −3
Let the n^th term of the given AP be the first negative term.
Then T_n < 0
⇒ a + (n −1)d < 0
⇒ 20 + (n − 1) ⨯ (−3) < 0
⇒ 23 − 3n < 0
⇒ 23 < 3n
⇒ n > 7.6
∴ n = 8
Hence, the 8^th term of the given AP is the first negative term.