It is well known that if f is an entire function of exponential type less than log 2, then the sequence of Newton interpolating polynomials based on the data {f(k)}, k = 0, 1,…, converges. The convergence of this interpolation process for rational functions of first degree is investigated. The result is applied then to answer a recent question of Askey (this journal, 1993) concerning the nonnegativity of the sums ∑nk=0P(α,β)k(x)/P(β,α)k(1), -1 ⩽ x ⩽ 1, n=1,2,….