Answer:
[tex]a_ {1}=2 \\ a_ {n + 1}= \frac{2}{3} a_ {n } [/tex]
Step-by-step explanation:
The sequence is defined explicitly as
[tex]a_n=3( \frac{2}{3} )^n[/tex]
The first term of this sequence is
[tex]a_1=3( \frac{2}{3} )^1 = 2[/tex]
The recursive formula is given as:
[tex]a_n=ra_ {n - 1}[/tex]
Or
[tex]a_ {n + 1}=ra_ {n }[/tex]
where
[tex]r = \frac{2}{3} [/tex]
is the common ratio.
The recursive formula is therefore:
[tex]a_ {1}=2 \\ a_ {n + 1}= \frac{2}{3} a_ {n }[/tex]
