What is the equation for the asymptote of the following function? f(x)=-2^-x+5

Assuming that the given function is - 2 ^ (- x + 5) you need to find the limit of the function as x goes to negative infinity.

That is:

Lim x → ∞ of [ - 2^ ( - x + 5) ]

And the result is 0, meaning that the asymptote is y = 0.

You can observe the graph in the attached picture.

Well,

This could be an arithmetic sequence.
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
...

This could also be a geometric sequence.
1*3=3
3*2=6
6*1=6
6*0=0
0*-1=0
0*(anything)=0
...