Question

Is 184 a term of the AP 3, 7, 11, 15, ...?

Answer 1

The given AP is 3, 7, 11, 15,...

Here, a = 3 and d = 7 – 3 = 4

Let the nth term of the given AP be 184. Then,

`a_n = 184`

⇒ 3 + (n – 1) × 4 = 184   ...[a_n = a + (n – 1)d]

⇒ 4n – 1 = 184

⇒ 4n = 185

⇒ `n = 185/4 = 46 1/4`

But, the number of terms cannot be a fraction.

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