Simple Recurrence Questions

Question

$r$ is a real number, define a recurrence relationship for $A_n$

$$A_0 = 1\\ A_n = r\cdot A_{n-1}$$

Question: What is the value of $A_4$

1. $4(A{n-1})$
2. $r^4$
3. $1$
4. $4r$

I've pretty much eliminated answer choice #4

Answer 1

For the first question:

You know that $a_0=1$ and that $a_n = ra_{n-1}$. Plugging in $n=1$ means that $a_1 = ra_{1-1}$. Can you now calculate $a_1$? You say that $A_4 = 4(A_n-1)$, but this is a bad answer. What, here, is the value of $n$? See, If you ask me "how old are you", and I answer $24 x + 23$, why is this answer wrong? Because I haven't told you what $x$ is, right? Same with this answer, you cannot say $A_4=4(A_n-1)$ if you don't tell me what $n$ is.