For a set of positive and relative prime integers A, let Γ(A) denote the set of integers obtained by taking all nonnegative integer linear combinations of integers in A. Then there are finitely many positive integers that do not belong to Γ(A). For the modified arithmetic progression A = {a, ha + d, ha + 2d, ... , ha + kd}, gcd(a, d) = 1, we determine the largest integer g(A) that does not belong to Γ(A), and the number of integers n(A) that do not belong to Γ(A). We also determine the set of integers S*(A) that do not belong to Γ(A) which, when added to any positive integer in Γ(A), result in an integer in Γ(A). Our results generalize the corresponding results for arithmetic progressions.