Math

Sum of a Linear Number Sequence Calculator

Sum an arithmetic sequence from its first term, common difference and length.

Calculated Output

Sum 5,050

Last term 100

Formula: S = n/2 × (2a + (n − 1)d)

Step-by-Step Breakdown

1. Values used:

2. First term = 1

3. Common difference = 1

4. Number of terms = 100

6. Sum = 5,050

7. Last term = First term x Common difference x Number of terms = 1 x 1 x 100 = 100

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The math behind it

S = n/2 × (first + last), and the last term is a + (n − 1)d. This is the classic Gauss summation.

1 + 2 + … + 100 = 100/2 × (1 + 100) = 5050.

What is a linear sequence?

One where each term increases by a constant amount (the common difference).