Arithmetic Sequence Calculator (nth Term & Sum)
By Santaji GadepatilinUpdated November 4, 2026
An arithmetic sequence adds the same common difference d to get from one term to the next — 3, 7, 11, 15 and so on. This arithmetic sequence calculator finds the nth term and the sum of the first n terms, and can solve backwards for the first term, the difference or the number of terms.
How to use the arithmetic sequence calculator
Enter the first term, the common difference and the term number n. The calculator returns the nth term and the sum of the first n terms. To work backwards, clear any field and fill in the nth term or the sum — for example, find which term of a sequence equals a given value.
Arithmetic sequence formulas
aₙ = a₁ + (n − 1) d · Sₙ = n (a₁ + aₙ) ÷ 2
Example
First term 3, common difference 4, n = 10:
- a₁₀ = 3 + (10 − 1) × 4 = 39
- S₁₀ = 10 × (3 + 39) ÷ 2 = 210
Terms and running sums (a₁ = 3, d = 4)
| n | aₙ | Sₙ |
|---|---|---|
| 1 | 3 | 3 |
| 2 | 7 | 10 |
| 3 | 11 | 21 |
| 4 | 15 | 36 |
| 5 | 19 | 55 |
| 6 | 23 | 78 |
| 7 | 27 | 105 |
| 8 | 31 | 136 |
| 9 | 35 | 171 |
| 10 | 39 | 210 |
| 11 | 43 | 253 |
| 12 | 47 | 300 |
Notes
- A negative common difference gives a decreasing sequence.
- The terms of an arithmetic sequence grow linearly; for terms that grow by a constant ratio, use the geometric sequence calculator.
Frequently asked questions
What is the formula for the nth term of an arithmetic sequence?
aₙ = a₁ + (n − 1)d, where a₁ is the first term and d the common difference.
How do I find the sum of an arithmetic series?
Sₙ = n(a₁ + aₙ) ÷ 2 — the number of terms times the average of the first and last term. Equivalently Sₙ = n[2a₁ + (n − 1)d] ÷ 2.
How do I find the common difference?
Subtract any term from the next one — d = a₂ − a₁. From two known terms, d = (aₙ − aₘ) ÷ (n − m).
What is the sum of the numbers 1 to 100?
5,050 — with a₁ = 1, d = 1 and n = 100, Sₙ = 100 × (1 + 100) ÷ 2.