High 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 :

To solve this problem, we need to find the value of [tex]\( f(1) \)[/tex] based on the given recursive relationship and information.

1. Understand the Recursive Function:
The recursive function is defined as [tex]\( f(n+1) = \frac{1}{3} f(n) \)[/tex]. This means each term in the sequence is one-third of the previous term.

2. Given Information:
We are provided with [tex]\( f(3) = 9 \)[/tex].

3. Work Backwards to Find [tex]\( f(1) \)[/tex]:

- Determine [tex]\( f(2) \)[/tex]:
Since [tex]\( f(3) = \frac{1}{3} f(2) \)[/tex], we can express this as:
[tex]\[
f(2) = 3 \times f(3)
\][/tex]
Substitute the given [tex]\( f(3) = 9 \)[/tex]:
[tex]\[
f(2) = 3 \times 9 = 27
\][/tex]

- Determine [tex]\( f(1) \)[/tex]:
Similarly, using the recursive definition for the previous term:
[tex]\[
f(1) = 3 \times f(2)
\][/tex]
Substitute the known value [tex]\( f(2) = 27 \)[/tex]:
[tex]\[
f(1) = 3 \times 27 = 81
\][/tex]

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