Question

100 - 99 + 98 - 97 + 96 ect formula

Answer 1

You want a rule for the sequence?  Forgetting the signs for a moment, this is a simple arithmetic sequence where each term is one less than the previous term.  The common difference is then just -1, and the initial term is 100.  The rule for any arithmetic sequence is:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

Since a=100 and d=-1 we have:

a(n)=100-1(n-1), which we can simplify as:

a(n)=100-n+1

a(n)=101-n

Now the only thing that we need to correct is to have the signs of the numbers alternate between positive and negative.

Since the first term is positive, we could say -1^(n+1).  This expression will start out positive and will alternate back and forth from then onward.  Now we simply have to multiply our sequence by this coefficient...

a(n)=-1^(n-1)*(101-n)

The above will produce the sequence you have listed....

Answer 2

100 - 99 + 98 - 97 + 96 = 98