College

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 :

To solve this problem, we need to work backward through the recursive sequence using the information provided. We know that the function is defined by:

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

And we are given that [tex]\( f(3) = 9 \)[/tex]. Our goal is to find [tex]\( f(1) \)[/tex].

Let's go step by step:

1. Find [tex]\( f(2) \)[/tex]:

According to the recursive definition, to find [tex]\( f(n) \)[/tex] from [tex]\( f(n+1) \)[/tex], we can rearrange the formula:

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

We know [tex]\( f(3) = 9 \)[/tex], so let's calculate [tex]\( f(2) \)[/tex]:

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

2. Find [tex]\( f(1) \)[/tex]:

Similarly, using the same method, we need to find [tex]\( f(1) \)[/tex] from [tex]\( f(2) \)[/tex]:

[tex]\[ f(1) = 3 \times f(2) = 3 \times 27 = 81 \][/tex]

Therefore, the value of [tex]\( f(1) \)[/tex] is [tex]\(\boxed{81}\)[/tex].

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