[Math] Find the nth term of a recursive sequence

Question

I have a the following sequence:
$$\begin{gather}
a_1 = 3 \\
a_{n + 1} = 1 + \frac{a_n}{2}
\end{gather}
$$
How can I find the $a_n$ term?

Answer 1

Let $a_n=b_n +2$

Then. $b_{n+1}=\frac{b_n}{2}$ and $b_1=1$

So, $b_n=2^{1-n}$

So $a_n= 2 + 2^{1-n}$