Answer:
\(a_n=-\frac{1}{4} \cdot a_{n-1}\)
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.
Given the sequence:
-16, 4, -1, ...
This is a geometric sequence.
Here, \(a_1 = -16\) and \(r = -\frac{1}{4}\)
Since,
\(\frac{4}{-16} = -\frac{1}{4}\)
\(\frac{-1}{4} = -\frac{1}{4}\) ans so on .....
Substitute the given values we have;
\(a_n = a_{n-1} \cdot -\frac{1}{4} = -\frac{1}{4} \cdot a_{n-1}\)
⇒\(a_n = -\frac{1}{4} \cdot a_{n-1}\)
Therefore, the recursive formula for the following geometric sequence is, \(a_n = -\frac{1}{4} \cdot a_{n-1}\)
