A variant of the Hales-Jewett Theorem

It was shown by V. Bergelson that any set B with positive upper multiplicative density contains nicely intertwined arithmetic and geometric progressions: For each positive integer k there exist integers a,b,d such that $b(a+id{)}^j:i,j\in \text{nhat}k\subset B\mathrm{.}$ In particular one cell of each finite partition of the positive integers contains such configurations. We prove a Hales-Jewett type extension of this partition theorem.