**Definition: **a Geometric progression is a numerical sequence, the first member of which is nonzero, and each member, starting with the second, equal to the previous member, **multiplied by** the same number not equal to zero.

**Definition: **the Denominator of a geometric progression is constant for the sequence number , which is multiplied by each member.

— geometric progression,

— geometric progression,

— **geometric progression**

— **the denominator of a geometric progression**

## The characteristic properties of geometrical progression

**Property:** the Square of any member of a geometric progression (starting from the second term) equal to the product of the previous and the next members, and Vice versa, if you vlastiti specified, the sequence is a geometric progression.

## Formula of nth member of geometric progression

## Formula sum of first n members of a geometric progression

## Plan solve problems on geometric progression

- Everything that is said in the speech tasks (members progress their amount, etc.) expressed through the first term and the difference of progression.
- Make the equation (or system of equations) according to the problem. In the case when the task of the transition from a geometric progression to an arithmetic progression and Vice versa, to form equations of the normally used characteristic properties of progressions.

## Infinitely decreasing geometric progression

**Definition: **an Infinitely decreasing geometric progression is an infinite geometric progression, and the denominator of which modulus less than unity .

### Example

**Definition: **the Sum of infinitely decreasing geometric progression is a limit, towards which the sum of its first members, at infinite growth .

.

## The formula to calculate the sum of an infinitely decreasing geometric progression

### Example of finding the sum of an infinitely decreasing geometric progression

## Converting a recurring decimal in the usual

### Example

(as the sum of infinitely decreasing geometric progression with the first member and the denominator )