The common ratio of both the formulas is 3 and 2. The first formula is explicit and the second is the recursive formula.
What is the recursive rule?
A rule is defined such that its definition includes itself.
1.
The given sequence is
-2, -6, -18, -54
Common ratio ;
r = -6 / -2 = 3
[tex]a _ n =-2 (3) ^{n-1}[/tex]
This given formula is the explicit formula.
2.
The given sequence is
4, 8, 16, 32
Common ratio ;
r = 8 / 4 = 2
[tex]a_n = a_{n-1}.2\\\\a _1 = 4[/tex]
This given formula is the recursive formula.
Learn more about the recursive rule and explicit rules here:
https://brainly.com/question/12620593
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