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 (ratio 1/r).

Property 3: If a_1, ..., a_n and b_1, ..., b_n are both GP, then a_1b_1, a_2b_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 (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 a/(1-r) and the terms approach 0.