Answer:
[tex]a_n=a_{n-1}(\frac{1}{3})\\a_1=27[/tex]
Step-by-step explanation:
A recursive formula is a formula in which each term is based on the previous term.
In a geometric sequence, each term is found by multiplying the previous term by a constant.
To get from 27 to 9, then from 9 to 3, etc., we would multiply by 1/3. This makes the common ratio 1/3.
The recursive formula for a geometric sequence is
[tex]a_n=a_{n-1}(r)[/tex], where [tex]a_n[/tex] represents the general term, [tex]a_{n-1}[/tex], represents the previous term, and r represents the common ratio.
Plugging in our values, we have
[tex]a_n=a_{n-1}(r)[/tex]
We also have to indicate what the first term, a₁, is. In this sequence, it is 21. This gives us
[tex]a_n=a_{n-1}(\frac{1}{3})\\a_1=27[/tex]
