contestada

The recursive rule for a geometric sequence is given.

a1=6;an=1/4an−1



Enter the explicit rule for the sequence.

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ANSWER

The explicit formula is

[tex]a_n=6 {( \frac{1}{4} )}^{n - 1} [/tex]

EXPLANATION

The recursive formula for the given geometric sequence is

[tex]a_1=6;a_n= \frac{1}{4} a_{n-1}[/tex]

This implies that;

[tex]r = \frac{1}{4} [/tex]

The explicit rule is given by:

[tex]a_n=a_1 {(r )}^{n - 1} [/tex]

We substitute the given values to obtain;

[tex]a_n=6 {( \frac{1}{4} )}^{n - 1} [/tex]

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