Question

The recursive rule for a geometric sequence is given. a1=2; an=1/3a subscript (n−1) Enter the explicit rule for the sequence. an=

Answer 1

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

Step-by-step explanation

The recursive formula is given as:

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

where

`a_1=2`

The explicit rule is given by:

`a_n=a_1 {r}^(n-1)`

From the recursive rule , we have

`r = (1)/(3)`

We substitute the known values into the formula to get;

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

Therefore, the explicit rule is:

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