Is -150 a term of 11, 8, 5, 2, ………?

In above sequence,

8 - 11 = -3 and 5 - 8 = -3.

Hence, above sequence is an A.P. with common difference = -3.

Let -150 be n^th term of the A.P.

∴ a_n = -150

⇒ a + (n - 1)d = -150

⇒ 11 + (-3)(n - 1) = -150

⇒ 11 - 3n + 3 = -150

⇒ 14 - 3n = -150

⇒ -3n = -164

⇒ n = $\dfrac{164}{3} = 54\dfrac{2}{3}$.

Since, no. of terms cannot be in fraction.

Hence, -150 is not a term of 11, 8, 5, 2, ………