Answer:
f(n) = 2 × [tex]3^{n-1}[/tex]
Step-by-step explanation:
In order to write an explicit rule for a geometric function, you need to know the common ratio; you can find the common ratio by dividing two consecutive terms:
6 ÷ 2 = 3, 18 ÷ 6 = 3, 54 ÷ 18 = 3, etc..
Now you know the common ratio is 3. At this point you can write your explicit function following the rule f(n) = [1st term] × [common ratio]^(n-1):
f(n) = 2 × 3^(n-1)
