Question

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

Answer 1

Answer:  It is geometric progression .

Step-by-step explanation:

Since we have given that

the sequence i.e. $81,3,\frac{1}{9}$

where

$a=81\\\\r=\frac{a_2}{a_1}=\frac{3}{81}=\frac{1}{27}\\\\r=\frac{a_3}{a_2}=\frac{1}{3\times 9}=\frac{1}{27}$

Since it has common ratio instead of common difference ,

$d=a_2-a_1=3-81=-78\\\\d=a_3-a_2=\frac{1}{9}-3=\frac{1-27}{3}=\frac{-26}{3}\\\\\text{ so, there is no common difference i.e. }a_3-a_2\neq a_2-a_1$

Hence, it is geometric progression rather than arithmetic progression.