Sum of Arithmetic Progression Formula

TopAn arithmetic sequence is defined as a series of terms in additive manner that means every term of Arithmetic Progression except first term bears an additive constant to the term immediately preceding it. An arithmetic progression can be represented as a₁, a₂, a₃ …….. a_n where all terms from second term onwards can be written in some additive form. If 'd' is constant additive term known as common difference then a₂ = a₁ + d , a₃ = a₂ + d , a₄ = a₃ + d and so on . Now these are general terms which are used to represent an arithmetic progression. Sum of Arithmetic Progression Formula is given below:
S_n = n / 2 [2 * a + (n - 1) * d],
Now there are some important points regarding sum of arithmetic progression formula. Points are given below-
1. If there are three known variables in formula then fourth one can be calculated easily.
2. If sum of first 'n' terms of an arithmetic progression is Sn then n th term of arithmetic progression can be found with the help of following formula:
T_n = S_n – S_{n – 1},
Where T_n is n th term of arithmetic progression.
3. If sum of terms existing in arithmetic progression is given then selection of terms should be in following manner:
· If total number of terms are odd then,
Number of terms are 3 then terms should be assumed as a - d, a, a + d.
Number of terms are 5 then selection of terms should be a - (2 * d), a - d, a, a + d, a + (2 * d).
· If total number of terms are even then,
Number of terms are 4 then terms will be as a - (3 * d), a - d, a + d, a + (3 * d)
Number of terms are 6 then selection will be as a - (5 * d), a - (3 * d), a - d, a + d, a + (3 * d),
a + (5 * d),