Which term of the AP 25, 20, 15, ... is the first negative term?
In the given AP, the first term = a = 25
Common difference = d = 20 - 25 = - 5
To find: place of first negative term.
So, an < 0
Since, we know that
an = a + (n - 1) × d
∴ 25 + (n - 1) × (-5) < 0
⇒ 25 - 5n + 5 < 0
⇒ - 5n + 30 < 0
⇒ - 5n < - 30
⇒ 5n > 30
⇒ n > 6
∴ 7th term of the AP is the first negative term.