Accumulators, Counters, and Running Totals

An accumulator works because it lives outside the loop. You declare it once, before the loop starts, and give it a starting value that will not change the result: 0 for a sum, 0 for a count, 1 for a product. Then each pass through the loop body updates that same variable, usually with total += value or count++. Because the variable was declared outside, it keeps whatever value the last pass left it with. The loop does not rebuild it; it only adds to it. Starting a sum at 0 matters because adding anything to 0 leaves it unchanged on the very first pass, so the first real value gets counted correctly. Start it at 5 instead, and every sum comes out 5 too high.

A counter works the same way but tracks how many times something happened rather than a total amount. You still declare it outside the loop at 0, but instead of adding a changing value, you add 1 whenever some condition is true, like arr[i] % 2 == 0 for counting evens.

This connects to the trace tables you have been filling in: each row shows the accumulator's value after one more pass, so tracing a sum or count is really tracing how one variable changes step by step. It also sets up for loops that compute averages or search for extremes, which just add a division or a comparison on top of this same pattern.