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

To find: Whether -150 is term of the AP

Given: a = 11, d = 8 – 11 = - 3, a_n = - 150, n = ?

We know that a_n = a + (n – 1)d

where a_n = nth term of AP
a = first terms of AP
n = no. of terms of AP
d = common difference of AP

Applying the formula, we get

Or, - 150 = 11 + (n – 1)(- 3)

Or, (n – 1)(-3) = - 150 – 11 = - 161

Or, n – 1 = 161/3


n - 1 = 53.67

It is clear that 161 is not divisible by three and we shall get a fraction as a result. But number of term cannot be a fraction.

Hence, - 150 is not a term of the given AP.