Answer: It is geometric progression .
Step-by-step explanation:
Since we have given that
the sequence i.e. [tex]81,3,\frac{1}{9}[/tex]
where
[tex]a=81\\\\r=\frac{a_2}{a_1}=\frac{3}{81}=\frac{1}{27}\\\\r=\frac{a_3}{a_2}=\frac{1}{3\times 9}=\frac{1}{27}[/tex]
Since it has common ratio instead of common difference ,
[tex]d=a_2-a_1=3-81=-78\\\\d=a_3-a_2=\frac{1}{9}-3=\frac{1-27}{3}=\frac{-26}{3}\\\\\text{ so, there is no common difference i.e. }a_3-a_2\neq a_2-a_1[/tex]
Hence, it is geometric progression rather than arithmetic progression.
