Respuesta :

each term is negative and 1/4 of previous term
so the nth term is the n-1 term times -1/4

so
[tex]f(n)= \frac{-1}{4} f(n-1)[/tex]

Answer:

[tex]a_n=-\frac{1}{4} \cdot a_{n-1}[/tex]

Step-by-step explanation:

The recursive formula for the geometric sequence is given by:

[tex]a_n = a_{n-1} \cdot r[/tex]

where,

r is the common ratio terms.

Given the sequence:

-16, 4, -1, ...

This is a geometric sequence.

Here, [tex]a_1 = -16[/tex] and [tex]r = -\frac{1}{4}[/tex]

Since,

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

[tex]\frac{-1}{4} = -\frac{1}{4}[/tex] ans so on .....

Substitute the given values we have;

[tex]a_n = a_{n-1} \cdot -\frac{1}{4} = -\frac{1}{4} \cdot a_{n-1}[/tex]

⇒[tex]a_n = -\frac{1}{4} \cdot a_{n-1}[/tex]

Therefore, the recursive formula for the following geometric sequence is, [tex]a_n = -\frac{1}{4} \cdot a_{n-1}[/tex]