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]
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]