# What is Geometric Sequences ?

##### 1 Answer

Feb 1, 2015

A geometric sequence is given by a starting number, and a common ratio.

Each number of the sequence is given by multipling the previous one for the common ratio.

Let's say that your starting point is

If the starting point is

- If
#r=1# , the sequence is constantly equal to#a# ; - If
#r=-1# , the sequence is alternatively equal to#a# and#-a# ; - If
#r>1# , the sequence grows exponentially to infinity; - If
#r<-1# , the sequence grows to infinity, assuming alternatively positive and negative values; - If
#-1<r<1# , the sequence exponentially decreases to zero; - If
#r=0# , the sequence is constantly zero, from the second term on.