Q. 13.6( 14 Votes )

The first term of

Answer :

Given first term is ‘a’ and sum of first p terms is Sp = 0 we have to find the sum of next q terms

Total terms are p + q

So, sum of all terms minus the sum of the first p terms will give the sum of next q terms

But sum of first p terms is 0 hence sum of next q terms will be the same as sum of all terms

So, we have to find sum of p + q terms

Sum of n terms of AP is given by

Where a is first term and d is the common difference

Using the given hint

Required sum = Sp+q – Sp

Using Sn formula

Now we have to find d

We use the given Sp = 0 to find d

0 = 2a + (p – 1) d

Put this value of d in (i)

required sum

Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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

There are n A.M.sRD Sharma - Mathematics

If x, y, z are inRD Sharma - Mathematics

Insert 7 A.M.s beRD Sharma - Mathematics

The 10th</suRD Sharma - Mathematics

Insert five numbeRD Sharma - Mathematics

The 4th</supRD Sharma - Mathematics

Insert 4 A.M.s beRD Sharma - Mathematics

Show that x2RD Sharma - Mathematics

An A.P. consists RD Sharma - Mathematics

How many terms arRS Aggarwal - Mathematics