# Arithmetic Sequence

An arithmetic sequence or arithmetical progression is a sequence of numbers such that the differences between successive terms is a constant, **d**, called the common difference.

8, 3, −2, −7, −12, ...

3 − 8 = −5

−2 − 3 = −5

−7 − (−2) = −5

−12 − (−7) = −5

d = −5.

### Nth Term of an Arithmetic Sequence

1If the 1st term is known.

**a _{n} = a_{1} + (n − 1) · d**

8, 3, −2, −7, −12, ..

a_{n}= 8 + (n−1) (−5) = 8 −5n +5 = = −5n + 13

2If the value that occupies any other term of the sequence is known.

**a _{n} = a_{k} + (n − k) · d**

a_{4 }= −7 and d = −5

a_{n} = −7+ (n − 4) · (−5)= −7 −5n +20 = −5n + 13

### Arithmetic Series

An arithmetic series is the sum of an arithmetic sequence.

#### Example

Calculate the sum of the first 5 terms of the sequence: 8, 3, −2, −7, −12, ...

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