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Let a and b be positive integers with a \leq b. An (a,b)-triple is a set{x,ax+d,bx+ 2d}, where x,d \geq 1. Define T(a,b;r) to be the least positiveinteger n such that any r-coloring of {1,2...,n} contains a monochromatic(a,b)-triple. Earlier results gave an upper bound on T(a,b;2) that is a fourthdegree polynomial in b and a, and a quadratic lower bound. A new upper boundfor T(a,b;2) is given that is a quadratic. Additionally, lower bounds are givenfor the case in which a = b, updated tables are provided, and open questionsare presented.

New Bounds on van der Waerden-type Numbers for Generalized 3-term Arithmetic Progressions