Answer:
Explanation:
For the explicit formula, we would apply the formula shown below
an = a1r^n
where
a1 is the first term
r is the common ratio
n is the number of terms
From the information given,
a1 = 54
r = 36/54 = 24/36 = 2/3
By substituting these values into the formula, the explicit formula is
an = 54(2/3)^n
The recursive formula defines a term in terms of the preceding term. It is written as
[tex]\begin{gathered} a_n\text{ = a}_{n\text{ - 1}}\times r \\ a_n\text{ = a}_{n\text{ - 1}}\text{ }\times\frac{2}{3} \end{gathered}[/tex]
The recursive formula is
an = a(n - 1) x 2/3
where n ≥ 1
n - 1 is a subscript
a0 = 54
