Question

Please answer asap!

Answer 1

ANSWER

The explicit rule is:

$a_n=2{( \frac{1}{3} )}^{n - 1}$

EXPLANATION

The recursive rule is

$a_1=2$

and

$a_n= \frac{1}{3} a_ {n - 1}$

We can rewrite to get,

$\frac{a_n}{a_ {n - 1}} = \frac{1}{3}$

This implies that, the constant ratio is:

$r = \frac{1}{3}$

The explicit rule is given by:

$a_n=a_1 {r}^{n - 1}$

We substitute the values to obtain, the explicit rule as:

$a_n=2{( \frac{1}{3} )}^{n - 1}$