Sum of Finite Arithmetic Sequence

Arithmetic progression can be defined as a sequence of terms which is formed by addition of constant term known as common difference to every term for forming next term of series. That is difference between two consecutive terms of a series of Arithmetic Progression is constant and it is termed as common difference. An Arithmetic Series is formed by addition of common difference only, and it is represented by‘d’. An arithmetic sequence includes an infinite series as well as a finite series. sum of finite arithmetic sequence can be determined by different formulas. The nth term of sequence can be determined by formula a_n = a + (n - 1) d where ‘a’ is initial term of sequence and‘d’ is common difference and sum of finite arithmetic sequence is determined by formula:
 S_n = n/ 2 [2 a + (n - 1) d].
 Where 'S' is the sum of finite terms, 'n' is number of terms, 'a' is the initial or first term and’d’ is the common difference between terms. When last term of series is given then formula can be modified as
 S_n = n/ 2 [a + l],
Where, ‘a’ is again the initial term and 'l' is the last term of series. General term of series is represented as a_n = a_m + (n - m) d where a_n is nth term of series, 'n' and 'm' are number of terms.
An arithmetic series can be represented in two different ways that are as follows:
S_n = a + (a + d) + (a + 2d) +. . . . . . . . . . . +[ a+ (n - 1) d],
And S_n = [a_n – (n - 1) d] + [a_n – (n - 2) d] +. . . . . . . . + (a_n – d) + a_n.