Q:

Give recursive definition of sequence $a_n = 2^n, n=2,3, 4... where $ $a_1 = 2$

Give recursive definition of sequence $a_n = 2^n, n = 2, 3, 4... where $ $a_1 = 2$
I'm just not sure how to approach these problems. 
Then it asks to give a def for:
$a_n = n^2-3n, n = 0, 1, 2...$
Thanks for all the help!

A:

For the first one, write the term $a_{n+1}$ and compare it to $a_n$:
$$a_{n+1}=2^{n+1}=2\cdot2^n=2a_n$$
For the second one, repeat the process:
$$\begin{align}a_{n+1}&=(n+1)^2-3(n+1)\\
&=n^2+2n+1-3n-3\\
&=n^2-3n+2n-2\\
&=a_n+2(n-1)
\end{align}$$

