Number Sequence Calculator
Find any term or the total sum of an arithmetic or geometric sequence, and see the first few terms laid out.
A sequence where each term increases (or decreases) by a fixed amount, like 3, 7, 11, 15...
A sequence where each term is multiplied by a fixed ratio, like 2, 6, 18, 54...
How to Use the Number Sequence Calculator
Choose your sequence type
Pick Arithmetic if each term increases by a fixed amount, or Geometric if each term is multiplied by a fixed ratio.
Enter your starting values
Fill in the first term, the common difference (or ratio), and which term number you want to find.
Click Calculate
Get the exact term value, the sum of all terms up to that point, and a preview of the sequence itself.
Arithmetic and Geometric Sequences Explained
A number sequence is an ordered list of numbers that follows a specific pattern. The two most common types are arithmetic sequences, where the pattern is a fixed amount added each time, and geometric sequences, where the pattern is a fixed multiplier applied each time. Both show up constantly in math, finance, computer science, and nature, and this calculator handles finding any term or the running total for both types.
What Is an Arithmetic Sequence?
In an arithmetic sequence, each term is found by adding a constant value, called the common difference, to the previous term. The sequence 3, 7, 11, 15, 19... is arithmetic with a common difference of 4, since each term is 4 more than the one before it.
Sum of first n terms: Sₙ = (n÷2)(2a + (n−1)d)
Example: Find the 10th term of the sequence starting at 3 with a common difference of 4. a₁₀ = 3 + (10−1)×4 = 3 + 36 = 39. The sum of the first 10 terms: S₁₀ = (10÷2)(2×3 + 9×4) = 5×(6+36) = 5×42 = 210.
Arithmetic sequences model anything that changes by a fixed amount over regular intervals, like a savings account with fixed monthly deposits (ignoring interest), seating arrangements that increase by a set number per row, or simple linear growth patterns.
What Is a Geometric Sequence?
In a geometric sequence, each term is found by multiplying the previous term by a constant value, called the common ratio. The sequence 2, 6, 18, 54, 162... is geometric with a common ratio of 3, since each term is 3 times the one before it.
Sum of first n terms: Sₙ = a(1−rⁿ) ÷ (1−r), for r ≠ 1
Example: Find the 6th term of the sequence starting at 2 with a common ratio of 3. a₆ = 2 × 3⁵ = 2 × 243 = 486. The sum of the first 6 terms: S₆ = 2(1−3⁶) ÷ (1−3) = 2(1−729) ÷ (−2) = 2×(−728) ÷ (−2) = 728.
Geometric sequences model exponential growth or decay, like compound interest, population growth under ideal conditions, radioactive decay, or the spread of information through repeated sharing (each person sharing with a fixed number of new people).
How to Tell the Two Apart
The quickest test: look at the difference between consecutive terms. If it's constant (always the same number added), it's arithmetic. If the ratio between consecutive terms is constant (always the same number multiplied), it's geometric. In the sequence 5, 10, 15, 20, the difference is always 5, so it's arithmetic. In the sequence 5, 10, 20, 40, the ratio is always 2 (each term doubles), so it's geometric, even though both sequences start the same way.
Why Sequences Grow So Differently
Arithmetic sequences grow linearly, meaning they increase at a steady, predictable pace no matter how far along you go. Geometric sequences, when the ratio is greater than 1, grow exponentially, meaning the rate of growth itself keeps increasing. This is why compound interest (geometric) eventually outpaces simple interest (arithmetic) by an enormous margin over long time periods, even if they start with similar-looking numbers. Understanding which type of pattern you're dealing with is essential for accurately projecting values into the future, whether that's a financial forecast, a population estimate, or a simple math problem.
Why Use Our Number Sequence Calculator
Instant Results
Get your answer the moment you click Calculate, no waiting or reloading.
Term and Sum Together
Every calculation shows both the specific term and the running total.
100% Private
Everything runs in your browser. Your numbers are never stored or sent anywhere.
Works on Any Device
Fully responsive design, so it's just as easy to use on mobile as on desktop.
Shows the Sequence Preview
See the first several terms laid out, not just the final answer.
Completely Free
No sign-up and no limits. Use it as often as you need, at no cost.
Frequently Asked Questions
Arithmetic sequences add a fixed number to get the next term. Geometric sequences multiply by a fixed number to get the next term. This makes geometric sequences grow (or shrink) much faster over time.
Use aₙ = a + (n−1)d, where a is the first term, d is the common difference, and n is the term number you want.
Use aₙ = a × r^(n−1), where a is the first term, r is the common ratio, and n is the term number you want.
Yes. A negative common difference produces a decreasing arithmetic sequence, and a negative common ratio produces a geometric sequence that alternates between positive and negative values.
Every term stays the same as the first term, and the sum simply becomes the first term multiplied by the number of terms, since there's no actual growth happening.
No. All calculations happen locally in your browser, and nothing you enter is stored or transmitted.
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