# Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms.

Let a1 and a2 be the first terms of the two APs

Let d1 and d2 be the common difference of the respective APs.

Given: d1 = d2 and a1 = 3, a2 = 8

To find: Difference between the sums of their first 50 terms.

i.e. to find: (S2)50 - (S1)50

where (S1)50 denotes the sum of first 50 terms of first AP and (S2)50

denotes the sum of first 50 terms of second AP.

Now, consider (S1)50 = (50/2)[2a1 + (50 - 1)d1]

= 25 × [2(3) + 49 × d1]

= 25[6 + 49d1]

= 150 + 1225d1

Now, consider (S2)50 = (50/2)[2a2 + (50 - 1)d2]

= 25 × [2(8) + 49 × d2]

= 25[16 + 49d1]

= 400 + 1225d2

Now, (S2)50 - (S1)50 = 400 + 1225d2 - (150 + 1225d2)

= 400 - 150 ( d1 = d2 )

= 250

(S2)50 - (S1)50 = 250

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  Arithmetic Progression Tricks and QUIZ37 mins  Quiz | Group of Questions on General Term of an A.P49 mins  Become a Master of A.P. in 45 Minutes!!47 mins  Get to Know About Geometric Progression41 mins  NCERT | Solving Questions on Introduction of A.P42 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 