Q. 17 C5.0( 2 Votes )

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

24, 20, 16, 12, ... and – 11, – 8, – 5, – 2, ...

Answer :

1st AP = 24, 20, 16, 12, ...


Here, a = 24, d = 20 – 24 = –4


and 2nd AP = – 11, – 8, – 5, – 2, ...


Here, a = –11, d = –8 – (–11) = –8 + 11 = 3


According to the question,


24 + (n – 1)(–4) = –11 + (n – 1)3


24 – 4n + 4 = –11 + 3n – 3


28 – 4n = –14 + 3n


28 + 14 = 3n + 4n


7n = 42


n = 6


6th term of the given AP’s are same.


Now, we will find the 6th term


We have,


an = a + (n – 1)d


a6 = 24 + (6 – 1)(–4)


a6 = 24 + 5 × –4


a6 = 24 – 20


a6 = 4


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