Arithmetico-Geometric Series

Arithmetico-Geometric Series 

 
Definition: 
If each part of a series is the product of the terms of the terms of an arithmetic progression and the terms of a geometric progression, then the series is known as  the Arithmetico-Geometric series.

The terms of the  arithmetic progression in the general form are:-
 a,a+d,a+2d,a+3d, ....... a+(n-1)d and 

The terms of a geometric progression are 1,r,r²,r³, ... then the series 
a.1+(a+d).r+(a+2d).r²+...............+a+(n-1)d.r^n is called the arithmetico-geometric series.













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