Arithmetic Sequence Calculator
Calculate any term and the sum of the first n terms of an arithmetic sequence — a sequence where each term increases (or decreases) by the same fixed amount.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter the first term, common difference, and term number to calculate the nth term and the sum of the first n terms of an arithmetic sequence.
The fixed amount added to each term to get the next one.
Which term to find, and how many terms to include in the sum.
Your result
29
nth term
Sum of first n terms155
AI explanation
Formula
nth term = a₁ + (n−1)d; Sum = n/2 × (2a₁ + (n−1)d)Worked example
2, 5, 8, 11, ... find the 10th term
| Field | Value |
|---|---|
| First term (a₁) | 2 |
| Common difference (d) | 3 |
| Term number (n) | 10 |
| nth term | 29 |
| Sum of first n terms | 155 |
Assumptions
- The common difference is added consistently between every consecutive pair of terms.
Frequently asked questions
What is an arithmetic sequence?
It's a sequence of numbers where the difference between any two consecutive terms is always the same, called the "common difference" — for example, 2, 5, 8, 11 has a common difference of 3.
How is the sum of an arithmetic sequence calculated?
Sum = n/2 × (2a₁ + (n−1)d), which comes from pairing the first and last terms, the second and second-to-last, and so on — each pair adds up to the same total.
What if the differences aren't constant in my sequence?
Then it's not a simple arithmetic sequence — try the Number Sequence Calculator, which can detect whether a given list of numbers follows an arithmetic or geometric pattern.