Question

Which term of the AP 25, 20, 15,... is the first negative term?

Answer 1

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
⇒ n > 6
∴ n = 7

Hence, the 7^th term of the given AP is the first negative term.