Start with 

100, the first term.

100-1² = 100-1 = 99, the second term.

 99-2² =  99-4 = 95, the third term.

 95-3² =  95-9 = 86, the forth term.

Rule for getting the (n+1)st term:

Take the nth term and subtract n squared.

So the recursion formula is

a1 = 100, an+1 = an - n²

The general formula is

an = 100-

That's found by more advanced methods.

Edwin