#### Question For what value of n, are the nth terms of two A.Ps 63, 65, 67,.... and 3, 10, 17,.... equal?

#### Video Explanation

#### Explanatory Answer

The nth term of an arithmetic progression, a_{n} = a_{1} + (n – 1)d

##### The first series is 63, 65, 67, ………

The first term of the series is 63 and its common difference is 2.

Therefore, the nth term of the first AP = 63 + (n – 1)2

##### The second series is 3, 10 , 17 ………

The first term of the series is 3 and its common difference is 7

The nth term of the second AP = 3 + (n – 1)7

##### The nth term of both the APs are equal

Therefore, 63 + (n – 1)2 = 3 + (n – 1)7

60 = 5(n – 1)

60 = 5n – 5

65 = 5n

n = 13

The 13^{th} term of both the arithmetic progressions will be same.