Tannakian fundamental groups of blended extensions

Let A₁, A₂,A₃ be semisimple objects in a neutral tannakian category over a field of characteristic zero. Let L be an extension of A₂ by A₁, and N an extension of A₃ by A₂. Let M be a blended extension (extension panach\'ee) of N by L. Under very mild and natural hypotheses, we study the unipotent radical of the tannakian fundamental group of M. Examples where our results apply include the unipotent radicals of motivic Galois groups of any mixed motive with three weights. As an application, we give a proof of the unipotent part of the Hodge-Nori conjecture for 1-motives (which is now a theorem of Andr\'e in the setting of Nori motives) in the setting of any tannakian category of motives where the group Ext¹(1,Q(1)) is as expected.