Question

In an AP prove a that the mth term is the arthematic mean of (m+n)th term and
(m-n)th term , (m>n)

Answer 1

mth term is a+(m-1)d...
(m+n)th term is a+(m+n-1)d
(m-n)th term is a+(m-n-1)d

arithmetic mean of (m+n) and (m-n) terms is {a+(m+n-1)d+a+(m-n-1)d}÷2
{2a+2(m-1)d}÷2
a+(m-1)d
which is equal to mth term.