Q. 17 A5.0( 3 Votes )

For what value of n are the nth term of the following two A.P's the same. Also find this term

13, 19, 25, ... and 69, 68, 67, ...

Answer :

1st AP = 13, 19, 25, …


Here, a = 13, d = 19 – 13 = 6


and 2nd AP = 69, 68, 67, …


Here, a = 69, d = 68 – 69 = –1


According to the question,


13 + (n – 1)6 = 69 + (n – 1)(–1)


13 + 6n – 6 = 69 – n + 1


7 + 6n = 70 – n


6n + n = 70 – 7


7n = 63


n = 9


9th term of the given AP’s are same.


Now, we will find the 9th term


We have,


an = a + (n – 1)d


a9 = 13 + (9 – 1)6


a9 = 13 + 8 × 6


a9 = 13 + 48


a9 = 61


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
NCERT | Fundamental Theorem Of Arithmetic45 mins
Fundamental Theorem of Arithmetic- 143 mins
Quiz on Arithmetic Progression Quiz32 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Arithmetic Progression Tricks and QUIZ37 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