D. f(9) = f(8) • (−4) is correct
Step-by-step explanation:
Given sequence is:
2, −8, 32, −128, …
As the sequence is geometric, we have to find the common ratio first. Common ratio is denoted by r.
So,
Here
[tex]a_1=2\\a_2=-8\\a_3=32\\a_4=-128\\r=\frac{a_2}{a_1}=\frac{-8}{2}=-4\\\frac{a_3}{a_2}=\frac{32}{-8}=-4[/tex]
The common ratio is -4.
The recursive formula is s formula that is used to calculate the next term by using the previous term.
In the case of geometric sequence, the recursive formula includes the previous term and common ratio to calculate the next term.
The general form is:
[tex]a_n=a_(n-1)*r[/tex]
It can also be written as:
[tex]f(n)=f(n-1)*r[/tex]
Out common ratio for given geometric sequence is -4. So,
[tex]f(n)=f(n-1)*-4[/tex]
So for 9th term, putting n=9
[tex]f(9)=f(9-1)*-4\\f(9)=f(8)*-4[/tex]
Hence,
D. f(9) = f(8) • (−4) is correct
Keywords: Geometric sequence, Recursive formula
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