1. A sequence of numbers is defined for every .

Prove that there are real numbers and such that for all natural number ,

I just plugged in the numbers and it works, as the problem just asked to find some real numbers. But that turns out to be the Lucas squence. In fact, the general answer states that

and

I just have no idea how s and t come.

2. A squence is defined as follows

for every

Find a formula for .

Again, the answer is

It looks like I need to apply the formula above, but how?

Thanks a lot!