Question

for what value of n are the nth term of two ap is 63,65,67 nad 3,10,17 equal?

Answer 1

nth term of first AP = 63 + (n-1)2 = 63 + 2n - 2 = 61 + 2n

nth term of second AP = 3 + (n-1)7 = 3 + 7n - 7 = 7n - 4

as the nth term of both APs are equal, therefore
                         
                   61 + 2n = 7n - 4
                         65 = 5n
therefore, n = 13 ;)

Answer 2

In the first a.p. a=63 and d=2
In the second a.p. a=3 and d=7
a+(n-1)d=A2+(n-1)D2
63+(n-1)2=3+(n-1)7
60+2n-2=7n-7
65=5n
n=13