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 ……


a = 1
d = 2
n = 30

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


= 900

Practise This Question

An antibiotic contains nitro group attached to aromatic nucleus in its structure. It is