Respuesta :

Answer:

a_n=-\frac{1}{4 a_{n-1}

Step-by-step explanation:

The recursive formula for the geometric sequence is given by:

a_n = a_{n-1} \cdot r

where,

r is the common ratio terms

-16, 4, -1, ...

This is a geometric sequence.

Here,  and

Since,

ans so on .....

Substitute the given values we have;

⇒

Therefore, the recursive formula for the following geometric sequence is,

Answer:

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

Step-by-step explanation:

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Here the common difference of two terms are not same.

LEts find the common ratio. To find common ratio, divide the second term by first term

[tex]\frac{4}{-16} =\frac{-1}{4}[/tex]

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

So common ratio is -1/4

Recursive formula is

[tex]A_n= A_{n-1} (r)[/tex]

'r' is the common ratio.

Recursive formula becomes

[tex]A_n= A_{n-1} (\frac{-1}{4})[/tex]

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