Answer:
[tex]a_{n}[/tex] = 18 [tex](\frac{1}{3}) ^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms, that is
[tex]\frac{6}{18}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 18 and r = [tex]\frac{1}{3}[/tex] , then
[tex]a_{n}[/tex] = 18 [tex](\frac{1}{3}) ^{n-1}[/tex]
