In an A.P (of even no. of terms) sum of all product of term taken equidistant from end and beginning is given by n?a^2+{2n-1}(3a+(n-1)d}d/3?

Abstract

This formula has been developed to calculate the sum of all product of term taken equidistant from end and beginning of an A.P(of even no. of terms). From this formula we can derive some properties of integers and natural no.