Q. 365.0( 13 Votes )

For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... are equal?

Answer :

Let a1 and d1 be the first term and common difference of the AP 63, 65, 67, 69,….

Let a2 and d2 be the first term and common difference of the AP 3, 10, 17,….


a1 = 63, d1 = 2


a2 = 3, d2 = 7


Let an be the nth term of the first AP and bn be the nth term of the second AP.


So, an = a1 + (n - 1)d1


an = 63 + (n - 1)2


an = 61 + 2n


and, bn = a2 + (n - 1)d2


bn = 3 + (n - 1)7


bn = - 4 + 7n


Since for nth terms of both the AP’s to be same, an = bn


61 + 2n = - 4 + 7n


61 + 4= 7n - 2n


65 = 5n


n = 13


Therefore, 13th term of both the AP’s will be same.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Lets Check Your Knowledge in A.P.49 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Quiz on Arithmetic Progression Quiz32 mins
Arithmetic Progression Tricks and QUIZ37 mins
Quiz | Group of Questions on General Term of an A.P49 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Become a Master of A.P. in 45 Minutes!!47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses