Q. 93.8( 20 Votes )

How many terms of the AP 9, 17, 25, ... must be taken so that their sum is 636?

Answer :

Here, first term = a = 9

Common difference = d = 17 - 9 = 8


Let first n terms of the AP sums to 636.


Sn = 636


To find: n


Now, Sn = (n/2) × [2a + (n - 1)d]


Since, Sn = 636


(n/2) × [2a + (n - 1)d] = 636


(n/2) × [2(9) + (n - 1)(8)] = 636


(n/2) × [18 + 8n - 8)] = 636


(n/2) × [10 + 8n] = 636


n[5 + 4n] = 636


4n2 + 5n - 636 = 0


4n2 + 5n - 636 = 0


(n - 12)(4n + 53) = 0


n = 12 or n = - 53/4


But n can’t be negative and fraction.


n= 12


12 terms of the given AP sums to 636.


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
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
Arithmetic Progression Tricks and QUIZ37 mins
Quiz | Group of Questions on General Term of an A.P49 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