Introduction to:GEOMETRIC SEQUENCE AND SERIES

Geometric Sequence

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,

The sequence 5, 10, 20, 40, 80, .... is an example of a geometric sequence. The pattern is that we are always multiplying by a fixed number of 2 to the previous term to get to the next term.

Be careful that you don't think that every sequence that has a pattern in multiplication is geometric. It is geometric if you are always multiplying by the SAME number each time.

nth or General Term of a Geometric Sequence

                    

where    is the first term of the sequence and r is the common ratio.

Geometric Series

It is a series of numbers or quantities in geometric progression.

There are two types of Geometric Series, the infinite and finite geometric series

The Sum of the First n Terms of aFinite Geometric Sequence

 is the first term of the sequence and r is the common ratio.

The Sum of an Infinite Geometric Series

If -1 < r < 1 (or  ), then the sum of the infinite geometric series 

in which   is the first term and r is the common ratio is given by 

If , the infinite series does NOT have a sum.