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 the problem, let's understand the sequence defined by the recursive function [tex]\( f(n+1) = \frac{1}{3} f(n) \)[/tex]. We know that [tex]\( f(3) = 9 \)[/tex] and we need to find [tex]\( f(1) \)[/tex].

1. Step 1: Find [tex]\( f(2) \)[/tex]
- According to the recursive relation, [tex]\( f(3) = \frac{1}{3} f(2) \)[/tex].
- We're given that [tex]\( f(3) = 9 \)[/tex].
- So, rearrange to find [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 3 \times f(3) = 3 \times 9 = 27
\][/tex]

2. Step 2: Find [tex]\( f(1) \)[/tex]
- Now use the recursive relation again, [tex]\( f(2) = \frac{1}{3} f(1) \)[/tex].
- We found [tex]\( f(2) = 27 \)[/tex].
- So, solve for [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 3 \times f(2) = 3 \times 27 = 81
\][/tex]

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

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