This:
sum=(limit*(2*1+(limit-1)*1))/ 2;
actually is the same as this formula:
where Sn denotes the sum of n terms, n is the number of terms(limit) and a1 is the first term of the AP and d is the common difference. All this information is found in the Wikipedia page for arithmetic progressions.
solved How the formula of a Arithmetic Progression works? [closed]
