Arithmetic Series Sum Calculator

Find the sum of an arithmetic series from the first term, common difference, and number of terms.

Input

Enter the first term, common difference, and number of terms to compute the sum of an arithmetic series, along with the last term, average, and leading sequence.

First term a

Common difference d

Number of terms n

The sum is S = n(2a + (n-1)d) / 2. The number of terms n must be a positive integer.

Result

Arithmetic series sum S

100

Last term (nth term)

Average

Number of terms

Start of the sequence

1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , ...

Last term = a + (n-1)d, sum S = n(first term + last term) / 2. The average is the midpoint of the first and last terms.

How it works

The nth term (last term) is a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.
The sum pairs the start and end of the series, giving S = n(2a + (n-1)d) / 2 = n(first term + last term) / 2.
The average equals the sum divided by the number of terms, which is exactly the midpoint between the first and last terms.
The number of terms n must be a positive integer. The first term a and common difference d may be decimals or negative numbers.

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