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

ANSWER

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

EXPLANATION

The recursive formula is given as:

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

where

$a_1=2$

The explicit rule is given by:

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

From the recursive rule , we have

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

We substitute the known values into the formula to get;

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

Therefore, the explicit rule is:

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