# Arithmetic Sequence Calculator

The first number (a) | |

common difference (d) | |

N^{th} term to obtain (n) |

## Arithmetic Sequence

### a_{n} = first term + a_{(n-1)} * d

A sequence is defined as arithmetic seqeunce "if the differences between the two consecutive term is same(constant)". Also, in the arithmetic sequence, by adding a fixed number to the previous term every term is obtained.

For example: 2,4,6,8,10,12..... is an arithmetic sequence.

## Arithmetic Sequence Formula

Let us assume the first term of an arithmetic sequence is a, its common difference is d and n is the number of terms. Then the general form of the AP is a, a+d, a+2d, a+3d,......up to n terms. There are different formulas associated with an arithmetic sequence used to calculate the nth term, the sum of n terms of an AP, or the common difference of a given arithmetic sequence.

- common difference(d) = a
_{2}- a_{1} - n
^{th}term = a+ a_{n-1}x d - sum of n terms = (n/2) (2a + (n-1) x d)

OR [a1+a_{n}] x d

## Arithmetic Sequence Example

Consider the sequence 2, 4, 6, 8, 10, .... is an arithmetic sequence because every term is obtained by adding a constant number (2) to its previous term.

- The first term, a = 2
- The common difference, d = 4 - 2 = 6 - 4 = 8 - 6 = 10 - 8 = ... = 2

Let's calculate the above example:

a, a + d, a + 2d, a + 3d, a + 4d, ... = 2, 2 + 2, 2 + 2(2), 2 + 2(3), 2 + 2(4),... = 2, 4, 6, 8, 10, 12.............