Determining the recurrence relation

Question

I am having trouble with this problem. I am trying to see if I am doing this properly, and it would be very helpful if someone could check my work.

Here is the problem:

A piece of paper is 1 inch thick. By folding it in half, the thickness becomes 2 inches. Folding into half again, its thickness becomes 4 inches,..

1. What recurrence relation is indicated?

2. What is the thickness of the paper after it is folded 10 times?

For 1, I did the following: $1,2,4,8,16\dots$ , $a_n=2^n$, $a_n=a_{n-1}\times2$, $a_1=1$.

For 2, I did the following: $1,2,4,8,16,32,64,128,256,512$, therefore the thickness of the paper after it is folded $10$ times is $512$ inches?

Answer 1

1. a_n = 2ⁿ , a_n-1 *2, a₁ =1

2. 1,2,4,8,16,32,64,128,256,512,1024, therefore the thickness of the paper after it is folded 10 times is 1024 inches.