Sum of Arithmetic Sequence Formula

About Sum of Arithmetic Sequence Formula

Let us first define an arithmetic sequence before learning about the sum of the arithmetic sequence formula. An arithmetic sequence is a set of integers in which each term is the sum of the terms before it and a fixed number. A common difference is the name given to this fixed number. As a result, the differences between every two successive terms in an arithmetic sequence are the same.

The formula for calculating the total of all the terms in an arithmetic sequence is known as the sum of the arithmetic sequence formula. We know that the addition of the members leads to an arithmetic series of finite arithmetic progress, which is provided by (a, a + d, a + 2d,...), where "a" is the first term and "d" is the common difference.

S_n= n/2[2a + (n-1)d]

S_n= n/2[a₁ + a_n]

Where,

S_n= the sum of the arithmetic sequence,

a₁= the first term,

d = the common difference between the terms,

n = the total number of terms in the sequence and

a_n= the last term of the sequence.