Q. 9

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

Answer :

Sum of the first n term is given by (sn) = [2a + (n-1) d]

The sum of first 7 terms S7 = 49 72


S7 = [2×a+(7-1)d]


49 = [2a+6d]


49 = 7[a+3d]


7 = a + 3d 1


The sum of first 17 terms S17 = 289 172


S17 = [2×a+(17-1)d]


289 = [2a+16d]


289 = 17[a+8d]


17 = a + 8d 2


By subtracting both the equations


17 – 7 = a + 8d – (a+3d)


10 = 5d


d =2


common difference (d) = 2


Substituting‘d’ in equation 1


7 = a + 3d


7 = a + 3(2)


a = 1


Sum of the first n term is given by (sn) = [2a + (n-1) d]


= [2×1 + (n-1)2]


= n[ 1+ (n-1)]


= n2


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 ProgressionChamp Quiz | Arithmetic ProgressionChamp Quiz | Arithmetic Progression34 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
caricature
view all courses
RELATED QUESTIONS :