The recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
Explanation:
The given sequence is [tex]\{-16,4,-1,........\}[/tex]
We need to determine the recursive formula for the given geometric sequence.
To determine the recursive formula, first we shall find the common difference.
Since, it is a geometric sequence, the common difference can be determined by
[tex]r=\frac{4}{-16} =-\frac{1}{4}[/tex]
[tex]r=-\frac{1}{4}[/tex]
Hence, the common difference of the given geometric sequence is [tex]r=-\frac{1}{4}[/tex]
The recursive equation for the geometric sequence can be determined using the formula,
[tex]a_n=r(a_{n-1})[/tex]
Substituting the value [tex]r=-\frac{1}{4}[/tex], we get,
[tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
Thus, the recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
