Answer :
Answer:
Option C) is correct
That is the given arithmetic sequence represents the recursive formula is f(n)=f(n-1)+(-5)
Step-by-step explanation:
The given arithmetic sequence is [tex]{\{94,89,84,79,...}\}[/tex]
Let f(1)=94,f(2)=89,f(3)=84,...
To find the common difference d :
[tex]d=f(2)-f(1)[/tex] ,
[tex]=89-94[/tex]
[tex]=-5[/tex]
Therefore d=-5
[tex]d=f(3)-f(2)[/tex] ,
[tex]=84-89[/tex]
[tex]=-5[/tex]
Therefore d=-5
Therefore the common difference d=-5
check the recursive formula [tex]f(n)=f(n-1)+d[/tex] which represents the given arithmetic sequence
Put n=2 and d=-5 in [tex]f(n)=f(n-1)+d[/tex] we get
[tex]f(2)=f(2-1)+(-5)[/tex]
[tex]=f(1)-5[/tex]
[tex]=94-5[/tex]
Therefore f(2)=89
Put n=3 and d=-5 in [tex]f(n)=f(n-1)+d[/tex] we get
[tex]f(3)=f(3-1)+(-5)[/tex]
[tex]=f(2)-5[/tex]
[tex]=89-5[/tex]
Therefore f(3)=84
and so on
Therefore the recursive formula [tex]f(n)=f(n-1)+d[/tex] where d=-5
Therefore the recursive formula [tex]f(n)=f(n-1)+(-5)[/tex] represents the given arithmetic sequence
Answer:
f(n) = f(n − 1) + (−5)
Step-by-step explanation:
The answer is C. I took the test and earned a 100%
