An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2008 and 2017 in which we have been asked to the value of n for which the nth terms of the arithmetic progressions 63, 65, 67,…..and 3, 10, 17, are equal?

RS Aggarwal, class 10, chapter 5A, question no 36

63,65,67…….

a=63,d=2

nth term =a+(n+1)d

=63+(n+1)2

=61+2n

(b)

3,10,17….

a=3,d=7

nth term =a+(n−1)d

=3+(n−1)7

=−4+7n

Now nth terms of 2 ap’s as equal

So 61+2n=7n−4

⇒5n=65

⇒n=13

13th term of APs are equal