Number Sequence Calculator
Generate the terms and sum of an arithmetic or geometric number sequence.
Each term adds 4 to the one before it, so the bars climb at a steady, constant rate.
- Sum of Terms210
- Sequence3, 7, 11, 15, 19, 23, 27, 31, 35, 39
About the Number Sequence Calculator
A number sequence is just a list of values that follows a fixed rule from one term to the next. The two most common patterns — arithmetic, where you add the same amount each time, and geometric, where you multiply by the same factor each time — cover most of what shows up in algebra classes and in real patterns: a savings account earning a flat monthly deposit, a population doubling on a fixed schedule, a ball bouncing to a fraction of its previous height on each bounce.
Students hit this mostly in algebra and precalculus, working out a specific term ("what's the 20th term?") or the sum of a run of terms without having to add or multiply them out one at a time by hand. Outside the classroom, the same math describes anything that grows or shrinks by a constant step or a constant ratio — loan balances, investment compounding, radioactive decay, and depreciation schedules are all sequences in disguise.
How it’s calculated
In an arithmetic sequence, each term is the previous term plus a fixed common difference d: aₙ = a₁ + (n−1)d. The sequence grows (or shrinks) by the same flat amount every step, so plotted out it forms a straight line.
In a geometric sequence, each term is the previous term multiplied by a fixed common ratio r: aₙ = a₁ × r^(n−1). Because the growth compounds instead of adding flatly, the terms curve — sharply upward if r is greater than 1, or shrinking toward zero if r is a fraction between 0 and 1.
The sum of the first n terms has a closed-form shortcut in both cases, which is what lets this calculator total up a sequence of any length instantly instead of adding every term one by one.
Frequently asked questions
What's the difference between an arithmetic and a geometric sequence?
Arithmetic sequences add a fixed amount to get the next term (2, 5, 8, 11…, adding 3 each time). Geometric sequences multiply by a fixed ratio instead (2, 6, 18, 54…, multiplying by 3 each time) — that's why geometric sequences grow so much faster.
How do I find the nth term of a sequence without listing every term?
Use the direct formula: aₙ = a₁ + (n−1)d for arithmetic, or aₙ = a₁ × r^(n−1) for geometric. Both let you jump straight to any term without computing everything before it.
What does a common ratio less than 1 do to a geometric sequence?
It shrinks the terms toward zero instead of growing them — each term is smaller than the last, which is exactly the pattern behind radioactive decay and value depreciation.
Can the common difference or ratio be negative?
Yes. A negative common difference makes an arithmetic sequence count downward, and a negative common ratio makes a geometric sequence alternate in sign from term to term while still growing or shrinking in magnitude.
Related calculators
Powered by GetCalculator.online