Question

Check whether -150 is a term of the A.P. 11, 8, 5, 2, …​

Answer 1

${\huge {\overbrace {\underbrace{\blue{ANSWER: }}}}}$

For the given series, A.P. 11, 8, 5, 2..

First term, a = 11

Common difference, d = a2−a1 = 8−11 = −3

Let −150 be the nth term of this A.P.

As we know, for an A.P.,

an = a+(n−1)d

=>-150 = 11+(n -1)(-3)

=>-150 = 11-3n +3

=>-164 = -3n

=>n = 164/3

=>n=54.67

Clearly, 

n is not an integer but a fraction.

Therefore,

– 150 is not a term of this A.P.

Answer 2

$\huge\red{\boxed{\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}}}$

a+(n-1)d=(-150)
11+(n-1)(-3)=-150
(n-1)(-3)=-161
n-1 = 53.666

So value of n is not a whole number.
So -150 is not the term of AP