Q. 363.6( 13 Votes )

The sum of the 4th and the 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the sum of its first 10 terms.

Answer :

Let a be the first term and d be the common difference.

Given: a4 + a8 = 24


and a6 + a10 = 44


To find: S10


Now, Consider a4 + a8 = 24


a + 3d + a + 7d= 24


2a + 10d = 24 ………….(1)


Consider a6 + a10 = 44


a + 5d + a + 9d = 44


2a + 14d = 44 ………..(2)


Subtracting equation (1) from equation (2), we get,


4d = 20


d = 5


Common difference = d = 5


Thus from equation (1), we get,


a = - 13


Now, Sum of first n terms of an AP is


Sn = [2a + (n - 1)d]


Sum of first 10 terms is given by:


S10 = [2(-13) + (10 - 1)(5)]


= 5 × [ - 26 + 45]


= 5 × 19


= 95


S10 = 95


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