a sequence is defined by the recursive function $f(n + 1)=\frac{1}{3}f(n)$. if $f(3)=9$, what is…
a sequence is defined by the recursive function $f(n + 1)=\frac{1}{3}f(n)$. if $f(3)=9$, what is $f(1)$?\n1\n3\n27\n81
Answer
Explanation:
Step1: Find $f(2)$ from $f(3)$
Given $f(n + 1)=\frac{1}{3}f(n)$, when $n = 2$, $f(3)=\frac{1}{3}f(2)$. Since $f(3)=9$, then $9=\frac{1}{3}f(2)$, so $f(2)=9\times3 = 27$.
Step2: Find $f(1)$ from $f(2)$
When $n = 1$, $f(2)=\frac{1}{3}f(1)$. Since $f(2)=27$, then $27=\frac{1}{3}f(1)$, so $f(1)=27\times3=81$.
Answer:
81