Question

check whether - 150 is a term of AP 11 8 5 2

Answer 1

let's take an=150 ,a=11,d=8-11=-3
so, an = 11+(n-1)-3
=11+(-3n+3)
=11-3n+3
=14-3n
14-3n=150
-3n=150-14
n=150-14/-3
n=136/3
so, 150is not term of these ap

Answer 2

Given
a=11
d=8-11
d= -3
an=-150
n=?
we know that
an= a+(n-1)d
-150= 11+(n-1)-3
-150-11=(n-1)-3

(n-1)-3= -161
-3n+3 =-161

-3n = -161 - 3
-3n = -164
n = 164 /3

But n should be a positive integer

So -150 is not a term of the given AP

Hope you helpful