Let a₁ and d₁ be the first term and common difference of the AP 63, 65, 67, 69,….

Let a₂ and d₂ be the first term and common difference of the AP 3, 10, 17,….

∴ a₁ = 63, d₁ = 2

a₂ = 3, d₂ = 7

Let a_n be the n^th term of the first AP and b_n be the n^th term of the second AP.

So, a_n = a₁ + (n - 1)d₁

⇒ a_n = 63 + (n - 1)2

⇒ a_n = 61 + 2n

and, b_n = a₂ + (n - 1)d₂

⇒ b_n = 3 + (n - 1)7

⇒ b_n = - 4 + 7n

Since for nth terms of both the AP’s to be same, a_n = b_n

⇒ 61 + 2n = - 4 + 7n

⇒ 61 + 4= 7n - 2n

⇒ 65 = 5n

⇒ n = 13

Therefore, 13^th term of both the AP’s will be same.