Which term of the A.P. 3, 8, 13,… is 248 ?

Given A.P is 3, 8, 13,…

Here, a₁ = a = 3, a₂ = 8

Common difference, d = a₂ – a₁ = 8 – 3 = 5

We know, a_n = a + (n – 1)d where a is first term or a₁ and d is common difference

∴ a_n = 3 + (n – 1)5

⇒ a_n = 3 + 5n – 5

⇒ a_n = 5n – 2

Now, to find which term of A.P is 248

Put a_n = 248

∴ 5n – 2 = 248

⇒ 5n = 248 + 2

⇒ 5n = 250

⇒ n = 50

Hence, 50^th term of given A.P is 248