Solve :

Is -150 a term of the arithmetic progression 11, 8, 5, 2, .… ?

The arithmetic progression is 11, 8, 5, 2, ….
Here, First term a = 11 and common difference = 8 – 11 = -3
Let us assume that n^th term a_n of the progression is -150.
Since, a_n = a + (n -1)d

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

∴ -150 = 11 + (n – 1) × (-3)
⇒ -150 = 11 - 3n + 3
⇒ -150 -14 = -3n
⇒ -164 = -3n
⇒ n = 54.667
Here n is a fraction, But any term n should be an integer.
∴ -150 is not any term of the arithmetic progression.

Hence, -150 is not any term of the progression.