The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
-16, 4, -1, ...
First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequence
Here
[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]
The recursive of geometric sequence is:
[tex]a_n = r * a_{n-1}[/tex]
Putting the value of r
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Hence,
The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Keywords: Geometric sequence, Recursive formula
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