Question

Pls answer the question no 28


Pls it’s urgent

Answer 1

Sm = m/2[2a + (m-1)d] ------(1)

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

As given, Sm = Sn, then,

m/2[2a +(m-1)d] = n/2[2a+(n-1)d]

am + m/2(m-1)d = an + n/2(n-1)d

m/2(m-1)d - n/2(n-1)d = an - am

[m²/2-m/2 - n²/2 + n/2]d = a(n-m)

[m²-n²/2 - 1( m-n)/2] d = -a(m-n)

[ (m+n)(m-n)/2 -1(m-n)/2] d = -a(m-n)

(m-n)/2 [ m+n-1]d = -a(m-n)

[m+n-1]d = -2a -------(3)

Now,

Sm+n = m+n/2[2a +(m+n-1)d]

Sm+n = m+n/2 [ 2a - 2a] (from eq 3).

Sm+n = m+n/2 × 0

Sm+n = 0