Middle School

We appreciate your visit to A sequence is defined by the recursive function tex f n 1 frac 1 3 f n tex If tex f 3 9 tex what. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A sequence is defined by the recursive function [tex]f(n+1) = \frac{1}{3}f(n)[/tex]. If [tex]f(3) = 9[/tex], what is [tex]f(1)[/tex]?

A. 1
B. 3
C. 27
D. 81

Answer :

Answer:

81 2020 edge

Step-by-step explanation:

Thanks for taking the time to read A sequence is defined by the recursive function tex f n 1 frac 1 3 f n tex If tex f 3 9 tex what. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Answer:

81

Step-by-step explanation:

[tex]f(n+1)=\frac{1}{3}f(n)[/tex] means a term can be found by multiplying previous term by [tex]\frac{1}{3}[/tex].

So if we want to go backwards to find the previous term from a term that comes after it we need to multiply that by [tex]3[/tex].

This means:

[tex]f(3)=9[/tex] implies [tex]f(2)=3(9)=27[/tex].

[tex]f(2)=27[/tex] implies [tex]f(1)=3(27)=81[/tex].

---------------------------------------------------------------------

Another way to look at it:

[tex]f(n+1)=\frac{1}{3}f(n)[/tex]

Multiply both sides by 3:

[tex]3f(n+1)=f(n)[/tex]

By the symmetric property:

[tex]f(n)=3f(n+1)[/tex]

So if [tex]n=2[/tex]:

[tex]f(2)=3f(2+1)[/tex]

[tex]f(2)=3f(3)[/tex]

[tex]f(2)=3(9)=27[/tex]

If [tex]n=1[/tex]:

[tex]f(1)=3f(1+1)[/tex]

[tex]f(1)=3f(2)[/tex]

[tex]f(1)=3(27)=81[/tex].