Which term of the A.P. 11, 8, 5, 2, ….. is −148 ?

1. 52nd

2. 54th

3. 55th

4. 57th

Given,

A.P. : 11, 8, 5, 2, …….

a = 11

d = 8 - 11 = -3

Let nth term of the A.P. be -148.

T_n = -148

⇒ a + (n - 1)d = -148

⇒ -148 = 11 + (n - 1)(-3)

⇒ -148 - 11 = (n - 1)(-3)

⇒ -159 = (n - 1)(-3)

⇒ $\dfrac{-159}{-3}$ = n - 1

⇒ n - 1 = 53

⇒ n = 53 + 1

⇒ n = 54.

Hence, option 2 is the correct option.