Which term of the AP is its first negative term?

Here, First term = a = 20

Common difference = d = (77/4) - 20 = (-3/4)

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

⇒ 20 + (n - 1) × (-3/4) < 0

⇒ 80 + (n - 1) × (-3) < 0 (multiplying both sides by 4)

⇒ 80 - 3n + 3 < 0

⇒ - 3n < - 83

⇒ 3n > 83

⇒ n > 27.66

Since n is an integer, therefore n must be 28.

∴ 28^th term will be the first negative term of the AP.