A sequence of numbers each one of which is equal to the preceding one multiplied by a number $q\ne0$ (the denominator of the progression). A geometric progression is called increasing if $q>1$, and decreasing if $0<q<1$; if $q<0$, one has a sign-alternating progression. Any term of a geometric progression $a_j$ can be expressed by its first term $a_0$ and the denominator $q$ by the formula
The expression
The term "geometric progression" is connected with the following property of any term of a geometric progression with positive terms: $a_n = \sqrt{a_{n-1}a_{n+1}}$, i.e. any term is the geometric mean of the term which precedes it and the term which follows it.