I found this interesting problem, well someone asked me, and I answered that on a whiteboard. But because I ran out of marker, I type the steps here. So that it will last longer. The problem goes like this (paraphrased): The sum of first 10 members of an Arithmetic progression is 110 . The sum of 11 th and 13 th terms is -4 . What is the sum of the first and second members ? It looks easy , maybe it can be done under 100 seconds. BUT, if we choose the wrong path , we should be be super sweating. Let's Translate That to Math Expressions First, Denotation Sum of n-finite series is usually denoted by $ S_n $. The $ n^{th} $ member (or term) is denoted by $ a_n $. The 1 st term is denoted by $ a $ (or to be consistent, $ a_1 $). To make it simpler, let's use $ a $. The difference between consecutive terms is denoted by $ d $ (as in difference ). Second, the Finite Arithmetic Formulas Arithmetic series (sum): ...