Which term of the AP 121, 117, 113, ... is its first negative term?

Question

Philoid · Accepted Answer

Here, First term = a = 121

Common difference = d = 117 - 121 = - 4

Let n^th term of the AP be its first negative term.

∴ a_n <0

Since, n^th term of an AP is given by:

a_n = a + (n - 1)d

∴ a + (n - 1)d < 0

⇒ 121 + (n - 1) × (-4) < 0

⇒ - 4n + 125 < 0

⇒ - 4n < - 125

⇒ 4n > 125

⇒ n > 31.25

Since n is an integer, therefore n must be 32.

∴ 32^nd term will be the first negative term of the AP.