Question

Write the explicit and recursive rules for the geometric sequence shown in the table.

Answer 1

Step-by-step 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

`\begin{gathered} a_n\text{ = a}_{n\text{ - 1}}* r \\ a_n\text{ = a}_{n\text{ - 1}}\text{ }*(2)/(3) \end{gathered}`

The recursive formula is

an = a(n - 1) x 2/3

where n ≥ 1

n - 1 is a subscript

a0 = 54