Check whether –150 is a term of the AP: 11, 8, 5, 2…

Let -150 is the \(n^{th}\) of AP 11, 8, 5, 2… which means that , \(a_n = -150\)

Here, First term = a = 11,
Common difference = d
= 8 – 11 = –3

Using formula \(a_n = a + (n - 1)d \), to find \(n^{th}\) term of arithmetic progression,

\(\Rightarrow\) -150 = 11 + (n - 1) (-3)
\(\Rightarrow \) -150 = 11 - 3n + 3
\(\Rightarrow \) 3n = 164
\(\Rightarrow \) n = \({{164} \over {3}}\)

But, n cannot be in fraction.

So, -150 is not a term of this A.P.