Using a geometric sequence, it is found that the missing terms of the table are, respectively, given by:
[tex]243, 1, \frac{1}{81}[/tex]
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
From the table, we get that the common ratio is of [tex]q = \frac{1}{3}[/tex], hence each term is the previous divided by 3, or the next multiplied by 3. Hence, the missing terms are given by:
[tex]3 \times 81 = 243[/tex]
[tex]3 \times \frac{1}{3} = 1[/tex]
[tex]\frac{1}{27} \times \frac{1}{3} = \frac{1}{81}[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
