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if sum of first p terms of a.p series is q and sum of first q series is p then what is sum of first (p+q) terms

if sum of first p terms of a.p series is q and sum of first q series is p then what is sum of first (p+q) terms

Grade:10

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
Dear student,

Lets assume
First term = a
and common difference = d

So , a + (p-1)d = q ….….…...(1)
and a + (q-1)d = p ….….…...(2)

From these 2 eqn solve for a and d

and put in this equantion
S(p+q)= a + (p+q-1)d

hence u will get ans
mycroft holmes
272 Points
5 years ago
The “expert’s “ answer is incorrect.
 
Solution is given below:
 
The sum of first n terms AP is of the form an2+bn for some constants a,b
 
We are given ap2+bp = q
                    aq2+bq = p
 
Subtracting, and dividing by (p-q) on both sides, you get
 
a(p+q)+b =-1
 
Now multiplying by (p+q) we have a(p+q)2+b(p+q) = -(p+q)
 
i.e.S(p+q) = -(p+q).
            

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