1. The problem statement, all variables and given/known data A step in this process of proving Sn: 1+4+7+...+(3n-2) = n(3n-1)/2 confuses me. I hope someone can clarify this for me. I do not require the work done, I need clarification on a step only. Thanks! 2. Relevant equations After assuming n=k, we say Sk: 1+4+7+...+(3k-2) = k(3k-1)/2 When assuming n=k+1, we say Sk+1: 1+4+7+...+(3k-2) + (3k+1) = k(3k-1)/2 + (3k+1) The book states the reason for adding (3k+1) on both sides of the equation is because 3(k+1)-2 = 3k+1 3. The attempt at a solution Why is this the case? What is 3(k+1)-2 ? I know it equals 3k+1 because 3 multiplied by (k+1) is 3k+3, then -2 makes it 3k+1. But where did 3(k+1)-2 suddenly come from? It seems arbitrary and is without explanation in the text book.