Given : The first A.P. is 63, 65, 67, ……

where a = , d = a₂ – a₁,

⇒ d = – =

and the second A.P. is 3, 10, 17, …….

where a = ; d = a₂ – a₁ = – =

Suppose the n^th terms of the two A.Ps are equal, where a_n = a + (n – 1)d

⇒ + (n – 1) = + (n – 1)

⇒ + n – = + n –

⇒ + n = n –

⇒ n – n = +

⇒ n =

∴ ^th terms of the two A.Ps are equal.