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A circuit training workout starts with a certain number of exercises and for each new exercise, decreases the number of repetitions by 1 (e.g. 20 squats, 19 pushups, 18 crunches, etc.) all the way down to 1 (e.g. the last exercise is 1 jumping jack). How many total repetitions are completed if there are n exercises?
One exercise
One total repetition
Two exercises
Three total repetitions
Three exercises
Six total repetitions
Four exercises
Ten total repetitions
Example Solution 1:
Example Solution 1:
It should be fairly clear that the number of total repetitions of all the exercises is the sum of consecutive integers. Check out the Sum of Integers solution for a "trick" on how to find this sum really quickly.
If we represent the problem visually in the correct way, we can also see connections to the solution of the Triangular Numbers problem.
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