Answer:
Option A) f(n)=-5-4n is correct.
The equation would produce the same sequence of numbers as the recursive formula is f(n)=-5-4n
Step-by-step explanation:
Given that a=-9 and [tex]a_{n}=a_{n-1}-4[/tex]
The recursive formula is [tex]a_{n}=a_{n-1}+d[/tex]
Therefore d=-4
Let [tex]a_{1}=-9[/tex] and d=-4
We can find [tex]a_{2},a_{3},...[/tex]
[tex]a_{2}=a_{1}+d[/tex]
[tex]=-9-4=-13[/tex]
Therefore [tex]a_{2}=-13[/tex]
[tex]a_{3}=a_{2}+d[/tex]
[tex]=-13-4=-17[/tex]
Therefore [tex]a_{3}=-17[/tex] and so on.
Therefore the arithmetic sequence is [tex]{\{-9,-13,-17,...}\}[/tex]
Option A) f(n)=-5-4n is correct.
f(n)=-5-4n
put n=1 in f(n)=-5-4n
f(1)=-5-4(1)
=-9
Therefore f(1)=-9
put n=2 in f(n)=-5-4n
f(21)=-5-4(2)
=-5-8
Therefore f(2)=-13
put n=3 we get f(n)=-5-4n
f(3)=-5-4(3)
=-5-12
Therefore f(3)=-17 and so on .
Therefore the sequence is [tex]{\{-9,-13,-17,...}\}[/tex]
Therefore the equation would produce the same sequence of numbers as the recursive formula is f(n)=-5-4n
