Counting Reps
When I do exercises in my gym, the number of repetitions often increases or decreases with each set. It often help to know the total number of repetitions so I can choose the correct weight. There is a simple formula to compute this, which you may already know, but is worth explainin for those who don't. And there is a story explaining it.
When the mathematician Carl Gauss was a boy, his teacher would tell students who had misbehaved to add the numbers one to a hundred as a punishment. One day this teacher told Carl Gauss to do this and was surprised when Carl came up to the teacher's desk with the correct answer. Carl had discovered a trick: when you reverse the numbers one to a hundred and it to the original, each pair sums to 101. Since there are one hunded pairs, this makes the total sum 100 times 101, or 10100. And since this is twice the original sum, if you divide by two, you gat the answer to the original problem, 5050.
So to compute the total repetitions of an exercise, add the number of repetitions for the first and last sets, multiply this sum by the total number of sets, and divide by two. This formula works whenever the number of repetitions increases or decreases by the same amount in each set.
As an example, Crossfit often does sets of 21, 15, and 9 repetitions. The sum of the first and last sets is 30 and there are 3 sets, so 3 times 30 is 90. Dividie by 2 to get the total repetitions, or 45 repetitions. You can verify this by adding 21, 15, and 9. Using this formula might be overkill for just three sets, but when the number of sets is greater, it shows its value. For example, yeserday we started with a set of 20 repetitions, going down by 2 each set. I completed through the set of 14. So my total reps was 20 plus 14 times 4 divided by 2, which is 68 repetitions.
As a special case, sometimes I do pyramid sets. You start with one repetition per set, go up by one each set to some number, and then go back to one. The first time I did this was with Dave's pushup ladder, which was one push per set up to ten pushups per set and then back to one. I admit this was too hard when I first tried it and I couldn't finish. But the total number of repetitions in any pyramid scheme is the highest number of repetitions squared. In the case of Dave's pushup ladder, that would be 100 total pushups. If you apply Gauss's formula, you can verify this. Sum the numbers zero to N with their reverse and you get N sets of N repetitions, or N squared total repetitions. So 1 to 5 is 25 total repetitions, 1 to 10 is 100 total repetitions, 1 to 15 is 225 total repetitions and anything more means you're doing too many.