Question

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?

Answer 1

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.

Answer 2

`"not geometric"`

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"`