Question

CBSE sample paper questions ....please solve this ques
1. If the sum of first m terms of AP is n and the sum of first n terms is m then show that the sum of first m+n terms is -(m+n).

Answer 1

HELLO DEAR,

LET a Be The First Term And d Be c.d. Of The A P .


THEN,


Sm=n



n= m/2{2a+ (m-1)d} 


2n= 2am+ m( m-1)d. ........(1)


and



Sn= m



m= n/2{2a+(n-1)d}



2m= 2an+ n(n-1)d. ...........(2)




Subtracting eq.(2)- (1),

we get



2a(m-1)+{m(m-1)- n(n-1)}d =

2n-2m



2a(m-n) +{(m^2-n^2)-(m-n)}




d = -2(m-n)




2a +(m+n-1) d = -2.

[On dividing both sides by


( m-n)]………(3) 



Now,



Sm+n=m+n/2{2a +(m+n-1)d}



Sm+n=m+n/2(-2) ………


[using (3)]



Sm+n=-(m+n)

I HOPE ITS HELP YOU DEAR,
THANKS