Arithmetic sequence formula is used to calculate the n^{th} term of an arithmetic sequence. To recall, a sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value. In other words, the difference between the adjacent terms in the arithmetic sequence is the same.

## Formulas of Arithmetic Sequence

For the formulas of an arithmetic sequence, it is important to know the 1st term of the sequence, the number of terms and the common difference. Now,

Arithmetic Sequence Formulas | |
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n^{th} Term Formula |
a_{n} = a_{1} + (n – 1)d |

Sum of First n Terms | S_{n }= n/2 (first term + last term) |

Where,

- a
_{n}= n^{th}term that has to be found - a
_{1}= 1^{st}term in the series n - n = the number of terms
- d = the common difference
- S
_{n}= the sum of n terms

A solved problem on the arithmetic sequence is given below.

### Solved Example Using Arithmetic Sequence Formula

**Question 1: **Find the 16^{th} term in arithmetic sequence 0, 2, 4, 6, 8, 10, 12, 14…..?** Solution: **

The arithmetic sequence is given as,

a_{n} = a_{1} + (n – 1)d

From the given problem,

a_{1} = 0 ;

n = 16 ;

d = 2

a_{16} = 0 + (16 – 1)2

a_{16} = 0 + (15 × 2)

a_{16} = 0 + 30

a_{16} = 30

More topics in Arithmetic Sequence Formula | |
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Sum of Arithmetic Sequence Formula | Arithmetic Sequence Explicit Formula |

Arithmetic Sequence Recursive Formula |