# Arithmetic series

A finite number of arithmetic sequence terms is called an arithmetic series. When we add them together we will get a sum of an arithmetic series.

When finding the sum of an arithmetic series, we need the first term, the last term and a quantity of terms

Find the sum for 1,2,3,4,5,6,7,8

We notice the sum of the first and the last term

1 + 8 = 9

the second and the second last

2 + 7 = 9

the third and the third last

3 + 6 = 9

and middle terms

4 + 5 = 9

The sum is 4 times 9 which is 36.

Because the arithmetic series always grows by the same amount and when viewed from the other end, the numbers always decreases by the same amount, so it is enough to add the first and last terms and multiply it by half of the quantity of terms, because there are always two terms in the sum. This consideration becomes the arithmetic series for the formula above.

Example 1

The first term of the arithmetic sequence is 2 and the second term is 5. Find the sum of the first ten terms.

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