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 ![a_{n}=a_{n-1}-4](/tpl/images/0459/7469/7539b.png)
The recursive formula is ![a_{n}=a_{n-1}+d](/tpl/images/0459/7469/9151d.png)
Therefore d=-4
Let
and d=-4
We can find ![a_{2},a_{3},...](/tpl/images/0459/7469/358ed.png)
![a_{2}=a_{1}+d](/tpl/images/0459/7469/88561.png)
![=-9-4=-13](/tpl/images/0459/7469/39602.png)
Therefore ![a_{2}=-13](/tpl/images/0459/7469/98571.png)
![a_{3}=a_{2}+d](/tpl/images/0459/7469/cc722.png)
![=-13-4=-17](/tpl/images/0459/7469/c7bc4.png)
Therefore
and so on.
Therefore the arithmetic sequence is ![{\{-9,-13,-17,...}\}](/tpl/images/0459/7469/88716.png)
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 ![{\{-9,-13,-17,...}\}](/tpl/images/0459/7469/88716.png)
Therefore the equation would produce the same sequence of numbers as the recursive formula is f(n)=-5-4n