Q. 425.0( 2 Votes )

The sum of the first 7 terms of an A.P. is 10, and that of the next 7 terms is 17. Find the progression.

Answer :

Given: Sum of first 7 terms, S7 = 10


and Sum of the next 7 terms = 17


Sum of 8th to 14th terms = 17


Sum of first 14 terms – Sum of first 7 terms = 17


S14 – S7 = 17


S14 – 10 = 17


S14 = 27


Sum of 7 terms,



20 = 7[2a + 6d]


20 = 14a + 42d …(i)


Sum of 14 terms,


27 = 7[2a + 13d]


27 = 14a + 91d …(ii)


Solving the linear equations (i) and (ii), we get


14a + 42d – 14a – 91d = 20 – 27


-49d = -7



Putting the value of d in eq. (i), we get


20 = 14a + 42d



20= 14a + 6


20 – 6 = 14a


14 = 14a


a = 1


Thus, a = 1 and


So, AP is


a1 = 1


a2


a3


Hence, AP is


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
Quiz on Arithmetic Progression Quiz32 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Fundamental Theorem of Arithmetic- 143 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