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

Question

Philoid · Accepted Answer

Here, First term = a = 3

Common difference = d = 7 - 3 = 4

Now, to check: 184 is a term of the AP or not.

Since, n^th term of an AP is given by:

a_n = a + (n - 1)d

If 184 is a term of the AP, then it must satisfy this equation.

So, let a_n = 184

∴ 184 = 3 + (n - 1) × 4

⇒ 184 - 3 = 4n - 4

⇒ 181 = 4n - 4

⇒ 181 + 4 = 4n

⇒ 4n = 185

⇒ n = 185/4 = 46.25

But this is not possible because n is the number of terms which can’t be a fraction.

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