Question

Prove that the sum of nth term from the beginning and nth term from the end of an A.P. is constant.

Answer 1

a = first term,
d = common difference,
l = last term.

Using the formula,

a_n = a + (n − 1)d

nth term from end = l − (n − 1)d

[a + (n − 1)d] + [l − (n − 1)d]

= a + l

The sum is a + l, which is independent of n.

The sum of the nth term from the beginning and the nth term from the end of an A.P. is constant.