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

Question

Philoid · Accepted Answer

In the given AP, the first term = a = 25

Common difference = d = 20 - 25 = - 5

To find: place of first negative term.

So, a_n < 0

Since, we know that

a_n = a + (n - 1) × d

∴ 25 + (n - 1) × (-5) < 0

⇒ 25 - 5n + 5 < 0

⇒ - 5n + 30 < 0

⇒ - 5n < - 30

⇒ 5n > 30

⇒ n > 6

∴ 7^th term of the AP is the first negative term.