Sum of Linear Sequence Calculator
Use our sum of linear sequence calculator to find the sum of a linear sequence (arithmetic sequence) quickly. Includes what is a linear sequence, the sum of linear sequence formula, the linear sum formula, and how to calculate sum of series step by step.
What is a Linear Sequence?
A linear sequence is a sequence where the difference between consecutive terms is constant. This is also called an arithmetic sequence.
If you’re asking what is a linear sequence, think of a pattern like 3, 7, 11, 15, … where each term increases by the same amount (+4).
The sum of a linear sequence is the total of the first n terms. This sum of linear sequence calculator uses the standard linear sum formula to compute it instantly.
Sum of Linear Sequence Formula
To calculate the sum of a linear sequence (arithmetic series), you can use the first term, last term, and number of terms, or use the first term and common difference.
Where a1 is the first term, an is the nth (last) term, and n is the number of terms.
Where d is the constant difference between terms.
This is how to calculate sum of series for a simple linear sequence.
Uses S_n = n/2 · (2a1 + (n-1)d).
How to Use the Sum of Linear Sequence Calculator
- 1
Enter the first term (a₁).
- 2
Enter the common difference (d) OR enter the last term (aₙ) if your calculator supports it.
- 3
Enter the number of terms (n).
- 4
The calculator returns the sum of the linear sequence using the sum of linear sequence formula.
Frequently Asked Questions
A linear (arithmetic) sequence is a sequence where the difference between consecutive terms is constant.
S_n = n/2 · (a_1 + a_n). Another equivalent form is S_n = n/2 · (2a_1 + (n-1)d).
Find a1, an (or d), and n, then apply S_n = n/2 · (a_1 + a_n).
For an arithmetic series: S_n = n/2 · (a_1 + a_n) or S_n = n/2 · (2a_1 + (n-1)d).
Yes—enter your sequence inputs and it outputs the sum instantly.