Which term of the A.P. 3, 10, 17, … will be 84 more than its 13th term?

Here, common difference = d = 10 - 3 = 7 and a = 3.

Let the nth term of A.P. be 84 more than its 13th term so,

⇒ a_n - a₁₃ = 84
⇒ a + (n - 1)d - (a + (13 - 1)d) = 84
⇒ 3 + 7(n - 1) - (3 + 12 × 7) = 84
⇒ 3 + 7n - 7 - (3 + 84) = 84
⇒ 7n - 4 - 87 = 84
⇒ 7n - 91 = 84
⇒ 7n = 84 + 91
⇒ 7n = 175
⇒ n = 25.

Hence, the 25th term of A.P. will be 84 more than 13th term.