Question

show that sum of (m+n)th term and (m-n)th terms of a.p is equal to twice the nth term

Answer 1

Given that twice the sum of ap is twice

Answer is given below

Answer 2

let the ap be a,a+d,a+2d,...
m/2{2a+m-1)d}=n
{2am+m(m-1)d}=2n..1
n/2{2a+(n-1)d}=m
{2an+n(n-1)d}=2mm...2
subtracting 2 from 1
2a(m-1)+[(m2-n2)-m-n}d=2(n-m)
2a+(m+n-1)d=-2....3
sm+n=m+n/2[2a+m+n-1)d]
m+n/2(-2)=-(m+n).....from 3