Arithmetic Sequence Calculator
Compute any term and the running total of an arithmetic progression from its first term, common difference, and term index.
Value of the nth term
- 1
Steps from first term
n − 1 = 10 − 1 = 9 - 2
Total increment (n−1) × d
9 × 3 = 27 - 3
nth term a₁ + (n−1)d
2 + 27 = 29
How does this calculator work?
For an arithmetic sequence the nth term is a_n = a1 + (n - 1)d and the sum of the first n terms is S_n = n/2 × (2a1 + (n - 1)d). Enter the first term, the common difference, and a whole-number index n to get the nth term, the running sum, and the last term instantly.
Formula
How this is calculated
An arithmetic sequence (or arithmetic progression) is a list of numbers where each term increases by a fixed amount called the common difference, d. You supply the first term a1, the common difference d, and the term index n (a positive whole number).
The nth term is found directly with a_n = a1 + (n - 1)d, since you add d a total of n-1 times after the first term. The sum of the first n terms is S_n = n/2 × (2a1 + (n - 1)d), which is equivalent to n/2 × (a1 + a_n) — the count of terms times the average of the first and last term. A positive d gives an increasing sequence and a negative d a decreasing one; d = 0 makes every term equal to a1.
The term index n must be an integer of 1 or more, so fractional or zero values are rejected. The plotted curves show each term and the cumulative partial sums; for very large n the chart caps the number of plotted points while the reported a_n and S_n remain exact.
Frequently asked questions
It is the constant amount added to each term to get the next one: d = a_(k+1) - a_k. It can be positive, negative, or zero.
Pairing the first and last terms gives n/2 pairs each summing to a1 + a_n, so S_n = n/2 × (a1 + a_n) = n/2 × (2a1 + (n - 1)d).
No. The term index counts terms, so it must be a whole number of 1 or greater. Decimal or zero values are not valid.
Also known as
TG we-Calculate Editorial Team. (2026). Arithmetic Sequence Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/arithmetic-sequence-calculator
TG we-Calculate Editorial Team. "Arithmetic Sequence Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/arithmetic-sequence-calculator.
TG we-Calculate Editorial Team, "Arithmetic Sequence Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/arithmetic-sequence-calculator
@misc{wecalculate_arithmetic_sequence_calculator, title = {Arithmetic Sequence Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/arithmetic-sequence-calculator}}, year = {2026}, note = {TG we-Calculate} }
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