Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?

Given: 3, 10, 17, 24, ...

First we need to calculate 13^th term.

We know that

a_n = a + (n – 1)d

Here, a = 3, d = 10 – 3 = 7 and n = 13

So, a₁₃ = 3 + (13 – 1)7

⇒ a₁₃ = 3 + 12 × 7

⇒ a₁₃ = 3 + 84

⇒ a₁₃ = 87

Now, the term is 84 more than a₁₃ is 84 + 87 = 171

Now,

a + (n – 1)d = 171

⇒ 3 + (n – 1)7 = 171

⇒ 3 + 7n – 7 = 171

⇒ 7n = 171 + 7 – 3

⇒ 7n = 175

⇒ n = 25

Hence, the 25^th term is 84 more than the 13^th term.