First A.P.: ( 3, 10, 17, \ldots )
( a = 3 ), ( d = 7 )
( a_n = 3 + (n-1)7 = 7n - 4 )

Second A.P.: ( 63, 65, 67, \ldots )
( a = 63 ), ( d = 2 )
( a_n = 63 + (n-1)2 = 2n + 61 )

Set equal: [ 7n - 4 = 2n + 61 ] [ 5n = 65 ] [ n = 13 ]

Answer: ( n = 13 )