The explicit formula for a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]
where r is the common ratio of the sequence.
For this sequence the common ratio is 2 and the first term is 2, therefore its explicit formula is:
[tex]f(n)=2(2)^{n-1}[/tex]
The recursive formula for a geometric sequence is given by:
[tex]\begin{gathered} f(1) \\ f(n)=rf(n-1) \end{gathered}[/tex]
Therefore in this case we have:
[tex]\begin{gathered} f(1)=2 \\ f(n)=2f(n-1) \end{gathered}[/tex]
