Question

Write each sequence as a function.

Answer 1

Answer: $f(n)=3^{n-1}$

Step-by-step explanation:

Given Recursive formula : $a_{n+1} = 3a_n,$, $a_1=1$

Then,  $a_2=a_{1+1} = 3a_1=3(1)=3$

$a_3=a_{2+1} = 3a_2=3(3)=9$

$a_4=a_{3+1} = 3a_3=3(9)=27$

We can write it as : $f(n)=3^{n-1}$

such that

n      $f(n)=3^{n-1}$

1       $f(1)=3^{1-1}=1$

2       $f(2)=3^{2-1}=3^1=3$

3       $f(3)=3^{3-1}=3^2=9$

Hence, the required function: $f(n)=3^{n-1}$

Answer 2

Answer:

$f(x)=3^x$ where $0\leq x$

Step-by-step explanation:

We are given that a sequence

$a_{n+1}=3a_n,a_1=1$

Where $n\geq 1$

We have to write a sequence as   function.

When n=1

$a_2=3a_1$

$a_2=3(1)=3$

n=2

$a_3=3a_2=3(3)=9=3^2$

$a_4=3a_3=3(9)=27=3^3$

$a_5=3(27)=81=3^4$

Therefore, the given sequence  can be write as function

$f(x)=3^x$ where $0\leq x$