College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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, we need to find the value of [tex]\( f(1) \)[/tex] for the given recursive sequence. The sequence is defined as [tex]\( f(n+1) = \frac{1}{3} f(n) \)[/tex]. We also know that [tex]\( f(3) = 9 \)[/tex].

Let's work backwards from the information provided:

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

We have the equation:
[tex]\[
f(3) = \frac{1}{3} f(2)
\][/tex]
Substitute [tex]\( f(3) = 9 \)[/tex]:
[tex]\[
9 = \frac{1}{3} f(2)
\][/tex]
To solve for [tex]\( f(2) \)[/tex], multiply both sides by 3:
[tex]\[
f(2) = 9 \times 3 = 27
\][/tex]

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

Next, use the equation:
[tex]\[
f(2) = \frac{1}{3} f(1)
\][/tex]
Substitute [tex]\( f(2) = 27 \)[/tex]:
[tex]\[
27 = \frac{1}{3} f(1)
\][/tex]
To solve for [tex]\( f(1) \)[/tex], multiply both sides by 3:
[tex]\[
f(1) = 27 \times 3 = 81
\][/tex]

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