Which term of the AP 53, 48, 43, … is the first negative term?

Given AP is 53, 48, 43, ….

Whose, first term, a = 53

common difference, d = 48 – 53 = - 5

Let nth term of the AP be the first negative term.

Then, we have to find the least value for which

a_n < 0

a + (n - 1)d < 0

53 + (n - 1) (- 5) < 0

53 - 5(n - 1) < 0

5(n - 1) > 53

so n will be least natural number greater than

i.e., 12th term is the first negative term of the given AP.