Add the first n terms of an arithmetic progression with a formula, the way young Gauss did, and use it for savings, seats, steps and stacks.
3 lessons, about 1 h 10 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabA long arithmetic progression can be added without adding its terms one by one. Write the terms forwards and backwards: every pair adds to the same number, . That gives , and the sum of is .
The sum formula can be used backwards. Given the sum, we can find how many terms make it, which leads to a quadratic equation, or find the first term or the common difference. And from a formula for , any term is .
Many everyday totals are sums of arithmetic progressions: money saved with a regular rise, seats in rows that grow, logs in a stack, prizes that fall by a fixed amount. The work is the same each time: find , and with their units, pick the right form of the formula, and check that the answer makes sense.
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