# How do you tell whether the sequence #-6, -2, -2/3, -2/9, -2/27# is geometric?

##### 1 Answer

May 3, 2017

see explanation.

#### Explanation:

#"the terms of a geometric sequence are"#

#a,ar,ar^2,ar^3, .... ,ar^(n-1)#

#"where r is the common ratio and"#

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

#" check r is common to the terms in this sequence"#

#(a_2)/(a_1)=(-2)/(-6)=1/3#

#(a_3)/(a_2)=(-2/3)/(-2)=1/3#

#(a_4)/(a_3)=(-2/9)/(-2/3)=1/3#

#rArr" sequence is geometric"#