Week 1 – Sum of arithmetic series

This week in Pre-Calc, we learned about finding the sum of an arithmetic series. An arithmetic series is the sum of all the terms in an arithmetic sequence. Using the formula makes it easier to find the sum without having to add up all the numbers 1 by 1.

To find the sum of an arithmetic series, you use the formula . N represents the amount of terms you have in your sequence . You replace  with the first term in your sequence and  with the last term in your sequence. When you have your formula ready, you add your first term and last term together and you divide ‘n’ by 2. Because you add the first and last term together, every other term going in the opposite direction should add to the same amount as the first and last.

Ex. 1 + 10 = 11, 2 + 9 = 11, 3 + 8 = 11

Because you’re adding the terms together, you divide the amount of terms you have in half and then multiply by the first and last term added together.

Ex. 10 ÷ 2 = 5, 5 (11) = 55

The total of the sequence would be 55