Geometric Progression: First Term and Common Ratio

A Geometric Progression (GP) is a sequence $T_1, T_2, T_3,\ldots$ in which the ratio of any term to the one immediately before it is always the same constant (and no term is zero). This constant is called the common ratio, denoted $r$:

The first term is again denoted $a$. Once $a$ and $r$ are known, the whole GP is determined by repeatedly multiplying by $r$: $a,\; ar,\; ar^2,\; ar^3,\ldots$

Example: in the GP $3, 6, 12, 24,\ldots$, the first term is $a=3$ and the common ratio is $r = \dfrac{6}{3}=2$ (checked again: $\dfrac{12}{6}=2$, $\dfrac{24}{12}=2$ — constant).