Let nth term of A.P. 3,10,17,… be an
And nth term of A.P. 63,65,67,…be an'
So,a1 = 3 and a2 = 10
∴ d = a2 - a1
= 10 - 3
= 7
And,
a1' = 63 and a2' = 65
∴ d' = a2' - a1' = 65 - 63 = 2
Now,
an = a1+(n-1)d
= 3+(n-1)7
= 3+7n-7
= 7n-4
And,
an'=a1'+(n-1)d'
= 63+(n-1)2
= 63+2n-2
= 2n+61
Now,
It is given that an = an'
∴ 7n-4 = 2n+61
∴ 7n-2n = 61+4
∴ 5n = 65
∴ n = 13