Question: I'm looking for help in finding the original equation behind a set of given answers:

when x = 100, the answer is 0.5 (1/2)
when x = 200, the answer is 0.6666 (2/3rds)
when x = 300, the answer is 0.75 (3/4ths)
when x = 400, the answer is 0.8 (4/5ths)

There is a pattern, and I tried approaching this problem as a Sequence, but could not get the differences to converge.

I cheated, and found the hidden formula (shown below) which governs the above sequence, but I still want to know how to reverse-engineer this problem so I could have found the "Hidden Formula" without looking up the answer.

Hidden Formula: x (x + 100)
so when x = 100, the formula would be: 100 (100 + 100) = 100 200 = 0.5

Thank you for any help you can give.