I see that derivative of y with respect to x is just like the ratio of y over x. But, Why Un (the formula to find nth term) is not the derivative of Sn (the sum of sequence formula) ?? For example, 1 2 5 10 -> y = x2+1 +1 +3 +5 -> y= 2x-1 +2 +2 -> y=2 I think that the second level is 2x (since it's the derivative of y = x2+1), but it's not... Derivative of y with respect to x is just like how much y will gain with x gaining, right ? Is there any way or formula to correlate the derivative of Sn with Un ??