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Arithmetic and geometric sequences follow simple, predictable patterns, but finding a specific term or the sum of many terms by hand gets tedious quickly.
This calculator finds the nth term and the sum of the first n terms for either an arithmetic or geometric sequence.
How it works
Choose arithmetic or geometric, then enter the first term, the common difference (arithmetic) or common ratio (geometric), and which term number you want. The calculator applies the standard nth-term and sum formulas for the chosen sequence type.
- Enter sequence type.
- Enter first term.
- Enter common difference (arithmetic) or ratio (geometric).
- Enter which term number (n)?.
- Click Calculate to see your results.
Examples
Arithmetic: 3, 8, 13, ...
An arithmetic sequence starting at 3 with a common difference of 5 has a 10th term of 48, and the sum of the first 10 terms is 255.
Geometric: 2, 6, 18, ...
A geometric sequence starting at 2 with a common ratio of 3 has a 5th term of 162, and the sum of the first 5 terms is 242.
Who should use it
- Solving arithmetic or geometric sequence problems for coursework.
- Quickly checking a hand-calculated sequence term or sum.
Industry applications
- Mathematics education
- Finance (geometric sequences underlie compound interest and annuities)
Advantages
- Handles both arithmetic and geometric sequences in a single calculator.
- Returns both the specific nth term and the running sum in one calculation.
Limitations
- Doesn't handle more complex sequence types (Fibonacci-style, quadratic, etc.).
Common mistakes to avoid
- Selecting the wrong sequence type for a given pattern — check whether the difference or the ratio between consecutive terms is constant.
- Confusing the common difference (arithmetic) with the common ratio (geometric) when entering the value.
Best practices
- Verify the sequence type by checking the first few terms: constant difference means arithmetic, constant ratio means geometric.
Tips
- Compound interest and loan amortization are both real-world applications of geometric sequences — this same math shows up throughout finance.