Question

for what value of n,the nth term of the two A.P s 63,65.67.... and 3,10,17.... are equal??

Answer 1

In first A.P

63 , 65 , 67 ......

a = 63

d = 2

To find nth term :-

an1 = a + ( n - 1 )d

an1 = 63 + ( n - 1 ) 2

an1 = 63 + 2n - 2


an1 = 61 + 2n


In second A.P

3 , 10 , 17 ......


a = 3

d = 7

an2 = a + ( n - 1 )d

an2 = 3 + ( n - 1 )7

an2 = 3 + 7n - 7

an2 = 7n - 4

Given in the question that an1 = an2


61 + 2n = 7n - 4

61 + 4 = 7n - 2n

65 = 5n

13 = n

So, for the 15th term the Value of A.P will be same in both the A.P