Question: I'm doing math by doing practice problems in my textbook.

I was able to find the explicit formula for $a\_n$ such that $a\_{n+1}=a\_n+2^n$ (which is $2^k-1$) I understand the theorems, but I'm having trouble solving questions.

I'm stuck on the second problem already. How do I find the explicit formula for the sequence $a\_n$ that's defined by recurrence relation $a\_{n+2}=a\_{n+1}+2a\_n$ and $a\_0=a\_1=1$? First of all, how do I even find a generating function?

Answer: 
The radius is $40 \text{ inches} = \frac{40}{12} \text{ feet}= \frac{10}3 \text{ ft}$ since $12 \text{ inches}=1\text{ foot}$. The wheel every second moves a distance equal to the arc length subtended by a $3$ radian angle on the wheel. The arc length is given by $3\cdot \frac{10}3\text{ feet}=10\text{ ft}$. So it moves $10 \text{ feet}$ in one second. The distance it moves in $1$ minute shouldn't be difficult to find.
V=r\*W 

where V= linear velocity, r= radius and W=angular velocity 

but first you need to convert inches to foot 

r= 40 inches = 10/3 foot

now V= r\*W = 10/3 \* 3 = 10 foot per sec

V= 600 foot per min

are you from US because never heard of using foot/min