Question

Is –150 a term of 11, 8, 5, 2, .......?

Answer 1

The given sequence is 11, 8, 5, 2, .......

Now,

8 – 11 = 5 – 8

= 2 – 5

= –3

Hence, the given sequence is an A.P. with first term a = 11 and common difference d = –3.

The general term of an A.P. is given by

t_n = a + (n – 1)d

${\displaystyle \Rightarrow }$ –150 = 11 + (n – 1)(–3)

${\displaystyle \Rightarrow }$ –161 = –3n + (–3)

${\displaystyle \Rightarrow }$ 3n = 164

${\displaystyle \Rightarrow n=\frac{164}{3}}$

The number of terms cannot be a fraction.

So, clearly, –150 is not a term of the given sequence.