Formula and calculator of the sum of an arithmetic progression

How to find the sum (S) of the first n numbers of an arithmetic progression on a calculator?

To calculate the sum of the members of an arithmetic progression on our calculator, you need to enter the following data: a known member of the arithmetic progression (be sure to indicate its place in the sequence), the step (difference) of the progression, the length of the arithmetic progression. After clicking the "Calculate" button, you will see an online output of the solution to this problem, as well as the sum of n numbers in the arithmetic progression. Our calculator can find the sum of up to 100 terms of a progression.

Formula for finding the sum of the first n terms of an arithmetic progression (Gauss formula):

S = ((a₁ + a_n) ÷ 2) × n, a_n – n-th term of the progression

a_n = a₁ + (n – 1) × d, a₁ – the first term of the progression, n is the number of terms of the progression, d is the step of the progression. This is the formula for finding the n-th term of a progression.

Formula for finding the sum of the terms of an arithmetic progression that begin not with the first term, but with the k term

S = ((a_k + a_n) ÷ 2) × (n – k + 1)