How do you determine whether the sequence #36, 27, 18, 9,...# is geometric and if it is, what is the common ratio?

1 Answer
Feb 26, 2017

Answer:

The series #36,27,18,9,.......# is not a geometric sequence, it is in fact arithmetic sequence.

Explanation:

In a geometric sequence, ratio of a term and its immediately preceding term is always constant.

In other words, to determine whether a sequence #a_1,a_2,a_3,a_4,a_5,.............# is a geometric sequence or not, one should check the ratios #a_2/a_1,a_3/a_2,a_4/a_3,a_5/a_4# and if they are all equal i.e.

#a_2/a_1=a_3/a_2=a_4/a_3=a_5/a_4#, then the sequence #a_1,a_2,a_3,a_4,a_5,.............# is a geometric sequence.

Here in the series #36,27,18,9,.......#

the ratios are #27/36,18/27,9/18#, which can be simplified to #3/4,2/3,1/2# and as ratios are different, the series #36,27,18,9,.......# is not a Geometric sequence.

Here, in fact we have #27-36=18-27=9-18=-9# and what we have is that they have common difference and hence the series #36,27,18,9,.......# is an arithmetic sequence.