# Sum of Arithmetic Sequence Formula

Arithmetic series of finite arithmetic progress is the addition of the members. The sequence that the arithmetic formula usually follows is (a, a + d , a + 2d, …) where 1 is the first term and d is the common difference. There are two ways with which we can find the sum of the arithmetic sequence.

We call S as the sum of the arithmetic sequence, a as the first term, d the common difference between the terms, n is the total number of terms in the sequence and L is the last term of the sequence.

The formula for the sum of arithmetic sequence below is:

$\large S=\frac{n}{2}(a+L)$

$\large S=\frac{n}{2}\left\{2a+(n-1)d\right\}$

### Solved example

Question: Find the sum of the first 30 terms of the sequence 1, 3 , 5 , 7, 9 ……

Solution:

Given,
a = 1
d = 2
n = 30

Using the formula: $S=\frac{n}{2}\left\{2a+(n-1)d\right\}$

$S=\frac{30}{2}\left\{2(1)+(30-1)2\right\}$

= 900

#### Practise This Question

Which of the following property of a proton can change while it moves freely in a uniform magnetic field?