# How do you determine whether the sequence #1, 1/2, 1/3, 1/4,...# is geometric and if it is, what is the common ratio?

##### 2 Answers

Jul 16, 2017

This is not a geometric progression. It is a harmonic one.

#### Explanation:

Examine to see if there's a common ratio:

#(1/2) / 1 = 1/2#

#(1/3) / (1/2) = 2/3#

#(1/4) / (1/3) = 3/4#

The ratio between successive terms is not common, so this is not a geometric sequence.

It is a harmonic sequence - the reciprocals of successive terms being in arithmetic progression.

Jul 16, 2017

#### Explanation:

#"for the sequence of terms to be geometric there must be a "#

#"common ratio (r) between them"#

#"where " r=(a_2)/(a_1)=(a_3)/(a_2)= ...... =(a_n)/(a_(n-1))#

#"here "r=(1/2)/1=1/2!=(1/3)/(1/2)=2/3#

#"sequence is therefore not geometric"#