# Manuals/calci/ARITHMETICSERIES

**ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)**

- is the starting value
- is the difference value of the series.
- is the positive real number.

## Description

- This function gives the Arithmetic series of the numbers.
- An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d.
- Therefore, for k>1,

```
.
```

- The sum of the sequence of the first n terms is then given by

## Examples

- ARITHMETICSERIES(10,3,6) = 10 13 16 19 22 25
- ARITHMETICSERIES(200,13/7,5) = 200 201.85714285714286 203.71428571428572 205.57142857142858 207.42857142857142
- ARITHMETICSERIES(33,-7,8) = 33 26 19 12 5 -2 -9 -16
- Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn(1,4,5) = 341
- Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn#; Sn(1,4..10,5)

a | r | n | Sn | |

1 | 4 | 5 | 341 | |

1 | 5 | 5 | 781 | |

1 | 6 | 5 | 1555 | |

1 | 7 | 5 | 2801 | |

1 | 8 | 5 | 4681 | |

1 | 9 | 5 | 7381 | |

1 | 10 | 5 | 1111 |

## Related Videos

## See Also

## References