Question

. If the sum of first m terms of an AP is the same as the sum of its first n terms, show that the
sum of its first (m + n) terms is zero.​

Answer 1

Answer:

Given,

Sn of first m terms of an AP = Sn of first nth term or an AP

show that,

Sn of (m+n)th = 0

1st,

Sn of mth term = m/2[2a+(m-1)d]

And,

Sn of nth term = n/2[2a+(n-1)d]

Sn of (m+n)th = 0

1/2{2am+md-d+2an+nd-d} = 0

0=0