# Arithmetic sequence

Calculates arithmetic progression terms from n to p.

Calculates the sum of terms from n to p.

You can enter numbers or fractions.

Calculates the sum of terms from n to p.

You can enter numbers or fractions.

## Arithmetic sequence

An arithmetic sequence, also called arithmetic progression, is a sequence of numbers in which each term is obtained by adding a constant to its preceding term. This constant is called the common difference.

The formula for the common difference is :

`d = U_(n+1) - U_n`

`U_(n+1)` is the (n+1)-th term of the sequence.

`U_n` is the n-th term of the sequence.

**Examples of arithmetic progression**

- The sequence of even numbers (0, 2, 4, 6, 8, 10 ...) is an arithmetic progression of first term 0 and common difference 2.

- The sequence of odd numbers (1, 3, 5, 7, 9, 11, 13 ...) is an arithmetic progression of first term 1 and common difference 2.

- The set of integers is an arithmetic progression of first term 0 and common difference 1.

**Calculation of the general term**

If `U_1` is the first term and d the common difference then, the general term formula is,

`U_n = U_1 + (n-1)*d`

If the first term is `U_p`, then the general term is equal to,

`U_n = U_p + (n-p)*d`

**Arithmetic sequence sum of terms**

The sum of the terms of a finite arithmetic sequence is called an arithmetic series. The arithmetic series formula is (with `U_1` being the first term),

`S_n = n * ( U_1+U_n )/2`