Math
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Arithmetic Sequence Calculator.
Calculate the nth term and sum of an arithmetic sequence.
Set your values
Results update as you type.
Results update automatically as you type.
Use Cases
Find any term in a sequence
Quickly determine the value of a specific term in an arithmetic progression without manually listing all previous terms.
Example: Find the 20th term of the sequence starting at 5 with a common difference of 3.
Calculate the sum of a series
Compute the total of the first n terms of an arithmetic sequence, useful for financial planning or mathematical problems.
Example: Sum the first 15 terms of the sequence 10, 7, 4, ...
Frequently Asked Questions
- What is an arithmetic sequence?
- An arithmetic sequence is a list of numbers where the difference between consecutive terms is constant. This constant is called the common difference. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.
- How do I find the nth term of an arithmetic sequence?
- The nth term is found using the formula: a_n = a_1 + (n - 1) * d, where a_1 is the first term, d is the common difference, and n is the term number. Simply enter these values into the calculator to get the result.
- How is the sum of an arithmetic sequence calculated?
- The sum of the first n terms is calculated using the formula: S_n = n/2 * (2a_1 + (n - 1) * d) or equivalently S_n = n/2 * (a_1 + a_n). The calculator uses the first term, common difference, and term number to compute this sum automatically.
Tips & Common Mistakes
Tips
- Ensure the common difference is consistent: subtract any term from the next to verify it matches.
- If the common difference is negative, the sequence decreases; the calculator handles negative values correctly.
- Use the term number as a positive integer; the calculator assumes n is a whole number.
- Double-check your inputs: the first term and common difference can be decimals or fractions.
Common Mistakes to Avoid
- Confusing the term number with the index: the first term corresponds to n=1, not n=0.
- Entering the common difference as the second term instead of the difference between terms.
- Using the wrong sign for the common difference when the sequence decreases.
Last updated: August 13, 2026