Q. 243.8( 4 Votes )

# If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first(p+q) terms.

Answer :

Given. For the A.P.

Sp = Sq

Let the first term = a, common difference = d

Therefore, according to the question =

Required. To find Sp + q

Now =

According to question

or p[2a + pd – d] = q[2a + qd – d]

or 2ap + p2d – pd = 2aq + q2d – qd

or 2a(p - q)2 +d(p2 – q2) – d(p –q) = 0

or 2a + d(p + q) - d = 0

2a + (p + q – 1)d = 0

Now Sp + q =

= = 0

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Sequence & Series (Lecture 1)56 mins
Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)37 mins
Interactive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 3| Interactive Quiz: Sequence & Series46 mins
Sequence & Series (Lecture 8)35 mins
Sequence & Series (Lecture 6)42 mins
Use of sigma in finding sum42 mins
Trigonometric Series45 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