Number Sequence Calculator
Find the nth term and sum of arithmetic and geometric sequences. See the first terms of any number pattern.
Term 10
32
Sum of first n terms
185
n = 10
First terms
5, 8, 11, 14, 17, 20, 23, 26, 29, 32
Arithmetic: each term adds the common difference.
Last updated: February 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Number sequences appear throughout Indian school mathematics, competitive exams and everyday finance, and this calculator handles both main types. Students preparing for board exams and entrance tests use it to verify nth term and sum formulas for arithmetic and geometric progressions. Financial planners model systematic savings with arithmetic sequences, where a fixed amount is added each month, and model compound interest with geometric sequences, where money multiplies by a fixed ratio each year. Scientists use geometric sequences to describe population growth, radioactive decay and cell division, and engineers encounter geometric progressions in digital file size calculations. Teachers use the tool to generate practice problems with known answers. By showing the nth term, the total sum and the first few terms at once, the calculator gives students the full answer set they need to check every part of a sequence question.
How to Use This Calculator
- Step 1: Choose whether your sequence is arithmetic (constant difference) or geometric (constant ratio).
- Step 2: Enter the first term of the sequence, such as 5.
- Step 3: Enter the common difference or ratio, such as 3, and the term number n, such as 10.
- Step 4: Read the nth term, the sum of the first n terms and a preview of the opening terms.
Worked Example
Priya, a college student in Pune, is saving for a laptop by increasing her monthly deposit. She starts with ₹5,000 and adds ₹500 more each month, an arithmetic sequence with first term 5,000 and common difference 500. After 12 months, the calculator shows the 12th term as 10,500, meaning her last deposit is ₹10,500, and the sum of all deposits is ₹93,000. Her friend studies a geometric example instead: a bacterial culture doubling from 2 to 6 to 18, with ratio 3. The 6th term is 486 and the sum of the first 6 terms is 728, showing how geometric growth races far ahead of arithmetic growth.
Tips and Common Mistakes
- •Tip 1: In an arithmetic sequence the gap between consecutive terms stays constant, which is the easiest way to recognise it.
- •Tip 2: For compound interest, savings or population growth, check whether a geometric model fits before assuming linear growth.
- •Tip 3: Use the preview of the first terms to confirm your sequence matches the pattern you intended before reading the final term.
- ✗Mistake 1: Entering a term number of zero, since sequences start at the first term, n = 1.
- ✗Mistake 2: Confusing the common difference with the common ratio, which turns an arithmetic problem into a completely different geometric one.
Frequently Asked Questions
What is an arithmetic sequence?
A sequence where each term differs from the previous one by a constant amount, called the common difference. For example, 5, 8, 11, 14 grows by 3 each step.
What is a geometric sequence?
A sequence where each term is the previous one multiplied by a constant ratio. For example, 2, 6, 18, 54 multiplies by 3 each time.
How is the nth term found?
For arithmetic, term n = first + (n − 1) × difference. For geometric, term n = first × ratio raised to (n − 1). The calculator applies these formulas for any n up to 1,000.
How is the sum of a sequence calculated?
The arithmetic sum is n/2 × (first + nth term). The geometric sum uses first × (ratioⁿ − 1) / (ratio − 1) when the ratio is not 1.
Where are sequences used in real life?
Arithmetic sequences model fixed monthly savings or salary increments, while geometric sequences model compound interest, population growth and loan repayments.
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