# Arithmetic series

An **arithmetic series** is a sum of consecutive terms in an arithmetic sequence. For instance,

is an arithmetic series whose value is 50.

## Contents

## Formula

To find the sum of an arithmetic sequence, we can write it out in two as so ( is the sum, is the first term, is the last term, and is the common difference): Flipping the right side of the equation we get

Now, adding the above two equations vertically, we get

This equals , so the sum is , where is the number of terms.

## Problems

### Introductory Problems

### Intermediate Problems

### Olympiad Problem

## See also

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