we have the sequence
27,9,3,1,1/3,1/9....
where
a1=27 first term
a2=9
a3=3
a4=1
a5=1/3
a6=1/9
Find out the ratio between consecutive terms
a2/a1=9/27=1/3
a3/a2=3/9=1/3
a4/a3=1/3
a5/a4=1/3/1=1/3
a6/a5=(1/9)/(1/3)=1/3
This is a geometric sequence
The common ratio is r=1/3
Find out the explicit formula for the nth term
The explicit formula is given by the expression
[tex]a_n=a_1(r)^{n-1}[/tex]we have
r=1/3
a_1=27
substitute
[tex]a_n=27(\frac{1}{3})^{n-1}[/tex]Find out the recursive formula for the nth term
The recursive formula is given by the expression
[tex]\begin{gathered} a_n=a_{n-1}(r) \\ r=\frac{1}{3} \\ \\ a_n=a_{n-1}(\frac{1}{3}) \end{gathered}[/tex]
