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

In the above A.P.,

a = 3 and d = 10 - 3 = 7.

⇒ a₁₃ = a + (13 - 1)d = 3 + 12(7) = 3 + 84 = 87.

Let n^th term be 84 more than its 13^th term.

⇒ a_n = 84 + a₁₃

⇒ a + (n - 1)d = 84 + 87

⇒ 3 + (n - 1)7 = 171

⇒ (n - 1)7 = 168

⇒ n - 1 = 24

⇒ n = 25.

Hence, 25^th term will be 84 more than its 13^th term.