Q. 184.5( 6 Votes )

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.?

Answer :

Given: a4 + a8 = 24 …(i)

a6 + a10 = 34 …(ii)

a4 = a + 3d

a8 =a + 7d

a6 =a + 5d

a10=a + 9d

Put the value of a4 and a8 in (i)

(a + 3d) + (a + 7d) = 24

a + 5d =12 …(iii)

Put the value of a6 and a10 in (ii)

(a +5d) + (a +9d) =34

a +7d =17 …(iv)

Subtracting (iii) from (iv), we get

2d = 5

d =

Putting the value of d in (iii), we get

a = 12 - =

Hence, first term is and common difference 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
Fundamental Theorem of Arithmetic- 143 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
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