Answer:
Explicit form: [tex]g_n=3(\frac{1}{3})^{n-1}[/tex]
Recursive form: [tex]g_n=\frac{1}{3}g_{n-1}[/tex] with [tex]g_1=3[/tex].
Step-by-step explanation:
The first term is 3 and we are dividing by 3 each time.
Another way to say we are dividing by 3 each time is to say we are multiplying by factors of 1/3.
If the first term is [tex]a[/tex] and [tex]r[/tex] is the common ratio then the geometric sequence in explicit form is:
[tex]a_n=a(r)^{n-1}[/tex]
[tex]g_n=3(\frac{1}{3})^{n-1}[/tex]
The recursive form for a geometric sequence is [tex]a_n=ra_{n-1}[/tex] with [tex]a_1=a[/tex] where [tex]r[/tex] is the common ratio and [tex]a[/tex] is the first term.
So the recursive form for our sequence is [tex]g_n=\frac{1}{3}g_{n-1}[/tex] with [tex]g_1=3[/tex].
