Question

Which explains why the sequence 81,3,1/9,... is arithmetic or geometric

Answer 1

Answer: It is geometric progression .

Explanation:

Since we have given that

the sequence i.e.
`81,3,(1)/(9)`

where

`a=81\\\\r=(a_2)/(a_1)=(3)/(81)=(1)/(27)\\\\r=(a_3)/(a_2)=(1)/(3* 9)=(1)/(27)`

Since it has common ratio instead of common difference ,

`d=a_2-a_1=3-81=-78\\\\d=a_3-a_2=(1)/(9)-3=(1-27)/(3)=(-26)/(3)\\\\\text{ so, there is no common difference i.e. }a_3-a_2\\eq a_2-a_1`

Hence, it is geometric progression rather than arithmetic progression.