Property 1: In a finite GP, the product of terms equidistant from beginning and end is constant: $a_1$ * $a_n$ = $a_2$ * $a_{n-1}$ = ... = a * l.

Property 2: If $a_1$, ..., $a_n$ is GP with ratio r, then $ca_1$, $ca_2$, ..., $ca_n$ is GP (same r). Also 1/$a_1$, 1/$a_2$, ..., 1/$a_n$ is GP $\frac{ratio 1}{r}$.

Property 3: If $a_1$, ..., $a_n$ and $b_1$, ..., $b_n$ are both GP, then $a_1$$b_1$, $a_2$$b_2$, ... is GP (ratio r1*r2). Also $a_1$/$b_1$, $a_2$/$b_2$, ... is GP.

Property 4: If a, b, c are in GP ($b^2$=ac), then:

• log a, log b, log c are in AP $\frac{log b = (log a + log c}{2}$)
• $a^n$, $b^n$, $c^n$ are in GP

Property 5: If each term of a GP is raised to the same power, the result is still GP.

Property 6: In an infinite GP with |r| < 1, the sum approaches $\frac{a}{1-r}$ and the terms approach 0.