Question

Please answer asap!

the recursive rule for a geometric sequence is given. a1=2 an=1/3an−1 enter the explicit rule for this sequence.

Answer 1

The explicit rule is:

`a_n=2{( (1)/(3) )}^(n - 1)`

Step-by-step explanation

The recursive rule is

`a_1=2`

and

`a_n= (1)/(3) a_ {n - 1}`

We can rewrite to get,

`\frac{a_n}{a_ {n - 1}} = (1)/(3)`

This implies that, the constant ratio is:

`r = (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{( (1)/(3) )}^(n - 1)`