# Arithmetic-Geometric Sequence An *Arithmetic-Geometric* sequence, or progression, is a sequence of ratios whose numerators form an [[Arithmetic Sequence]] and whose denominators form a [[Geometric Sequence]]. For example: $ \frac{1}{2} ,\frac{2}{4} ,\frac{3}{8} ,\frac{4}{16} , \ldots $ The common ratio is represented as a reciprocal value so for the common ratio $r$, common difference $d$, and initial term $a$, the general definition is $ a, (a+d)r, (a+2d)r^2, \ldots, [a+(n-1)d]r^{n-1} $ ![[Arithmetic-Geometric Series#^3peyiy]] ![[Arithmetic-Geometric Infinite Series#^a597aa]]