A new two-term relation for the 3F2 hypergeometric function of unit argument

The elementary manipulation of series together with summations of Gauss, Saalschutz and Dixon are employed to deduce a two-term relation for the hypergeometric function 3F2(1) and a summation formula for the same function, neither of which has previously appeared in the literature. The two-term relation has implications in the calculus of finite differences.