Answer:
Recursive: [tex]x_n=2(x_{n-1})[/tex]
Explicit: [tex]x_n=2(2)^{n-1}[/tex]
Step-by-step explanation:
First, note that this is a geometric sequence. This is because each term is 2 times its previous term.
The standard recursive form for a geometric sequence is:
[tex]x_n=r(x_{n-1})[/tex]
Where n is the nth term, so n-1 is the previous term, and r is the common ratio.
Substitute 2 for r.
Therefore, our recursive formula is:
[tex]x_n=2(x_{n-1})[/tex]
The standard form of the explicit formula for geometric sequences is:
[tex]x_n=ar^{n-1}[/tex]
Again, r is the common ratio and a is the initial term.
The common ratio is 2 and the initial term is 2. So, substitute:
[tex]x_n=2(2)^{n-1}[/tex]
And that's our explicit formula.
And we're done!
