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!
Answer :
Let's solve the problem step by step:
1. Understand the recursive function: We are given that the sequence is defined by the recursive relation [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. Use the given value: We are told that [tex]\( f(3) = 9 \)[/tex]. Based on the recursive relation, we can calculate the earlier terms in the sequence by working backwards.
3. Calculate [tex]\( f(2) \)[/tex]: Since [tex]\( f(3) = \frac{1}{3} f(2) \)[/tex], we can find [tex]\( f(2) \)[/tex] by multiplying [tex]\( f(3) \)[/tex] by 3:
[tex]\[
f(2) = 3 \times f(3) = 3 \times 9 = 27
\][/tex]
4. Calculate [tex]\( f(1) \)[/tex]: Similarly, since [tex]\( f(2) = \frac{1}{3} f(1) \)[/tex], we find [tex]\( f(1) \)[/tex] by multiplying [tex]\( f(2) \)[/tex] by 3:
[tex]\[
f(1) = 3 \times f(2) = 3 \times 27 = 81
\][/tex]
5. Conclusion: Therefore, based on these calculations, the value of [tex]\( f(1) \)[/tex] is [tex]\( 81 \)[/tex].
The answer is [tex]\( \boxed{81} \)[/tex].
1. Understand the recursive function: We are given that the sequence is defined by the recursive relation [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. Use the given value: We are told that [tex]\( f(3) = 9 \)[/tex]. Based on the recursive relation, we can calculate the earlier terms in the sequence by working backwards.
3. Calculate [tex]\( f(2) \)[/tex]: Since [tex]\( f(3) = \frac{1}{3} f(2) \)[/tex], we can find [tex]\( f(2) \)[/tex] by multiplying [tex]\( f(3) \)[/tex] by 3:
[tex]\[
f(2) = 3 \times f(3) = 3 \times 9 = 27
\][/tex]
4. Calculate [tex]\( f(1) \)[/tex]: Similarly, since [tex]\( f(2) = \frac{1}{3} f(1) \)[/tex], we find [tex]\( f(1) \)[/tex] by multiplying [tex]\( f(2) \)[/tex] by 3:
[tex]\[
f(1) = 3 \times f(2) = 3 \times 27 = 81
\][/tex]
5. Conclusion: Therefore, based on these calculations, the value of [tex]\( f(1) \)[/tex] is [tex]\( 81 \)[/tex].
The answer 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
