Question

If the sum of m th term of an AP is same as the sum of its n th term show that the sum of its m+n term is 0

Answer 1

Here is your answer ☺☺☺☺☺

Step-by-step explanation:

Sn=(n/2)(2a+(n-1)d) ....eq(i)

Sm=(m/2)(2a+(m-1)d) ....eq(ii)

Sm+n=((m+n)/2)(2a+(m+n-1)d) .....eq(iii)

given, Sn=Sm

therefore,

2am+dm^2-md = 2an+dn^2-nd

2a(m-n)+d(m^2-n^2-(m-n))=0

m-n(2a+d(m+n-1)=0

2a+d(m+n-1)=0 .... eq(iv)

from eq(iii) and eq(iv) we get

Sm+n=0