Question

The recursive rule for a geometric sequence is given.

a1=6;an=1/4an−1



Enter the explicit rule for the sequence.

Answer 1

6(1/4)^n-1

Explanation:

Answer 2

The explicit formula is

`a_n=6 {( (1)/(4) )}^(n - 1)`

EXPLANATION

The recursive formula for the given geometric sequence is

`a_1=6;a_n= (1)/(4) a_(n-1)`

This implies that;

`r = (1)/(4)`

The explicit rule is given by:

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

We substitute the given values to obtain;

`a_n=6 {( (1)/(4) )}^(n - 1)`