Question

Is 184 a term of the AP 3, 7, 11, 14, … ?

Answer 1

Given AP is 3, 7, 11, 14, …

First and second term of given AP are a₁ = 3, a₂ = 7 respectively.

The common difference of given AP is d = a₂ − a₁ = 7 − 3 = 4.

Let nth term of given AP is 184.

We know that nth term of AP is given by a_n = a₁ + (n - 1)d.

Since, 185 does not divide by 4, therefore, n does not have a positive integer value, therefore, such a term of AP is not possible. (For a term of AP, n must be a positive integer.)

Hence, 184 is not a term of the given AP.