# Arithmetic Sequence Formula

A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. Arithmetic Sequence 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.

**Arithmetic Sequence Formula –**

\[\LARGE a_{n}=a_{1}+(n-1)d\]

Where,

a_{n} – n^{th} term that has to be found

a_{1} – 1^{st} term in the seriesn

n- number of terms

d – common difference

Some solved problems on arithmetic sequence are given below:

### Solved Examples

**Question 1:**Find the 16

^{th}term in the arithmetic sequence 0, 2, 4, 6, 8, 10, 12, 14….. ?

**Solution:**

The arithmetic sequence is given as,

a

From the given problem,

a

a

a

a

a

a

_{n}= a_{1}+ (n – 1)dFrom the given problem,

a

_{1}= 0 ; n = 16 ; d = 2a

_{16}= 0 + (16 – 1)2a

_{16}= 0 + (15 $\times$ 2)a

_{16}= 0 + 30a

_{16}= 30More topics in Arithmetic Sequence Formula | |

Sum of Arithmetic Sequence Formula | Arithmetic Sequence Explicit Formula |

Arithmetic Sequence Recursive Formula |