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Build an arithmetic, geometric, or Fibonacci sequence and instantly see every term plus its total sum.
Example
Arithmetic with first term 2, common difference 3, and 6 terms:
Terms: 2, 5, 8, 11, 14, 17
Sum: 57
Last term: 17 Average: 9.5
Switching to Geometric with first term 3, ratio 2, 4 terms gives 3, 6, 12, 24 (sum 45).
How it works
Pick a sequence type, then enter the first term, the common difference/ratio (or second term for Fibonacci), and how many terms you want. The list and sum update live.
Good to know
The Number Sequence Calculator turns three inputs — a first term, a step value, and a term count — into a full sequence and its total. You choose one of three patterns: arithmetic (each term adds a fixed common difference), geometric (each term multiplies by a fixed ratio), or Fibonacci-style (each term is the sum of the previous two, starting from two seed values). It is aimed at students checking homework, teachers building examples, and anyone who needs the terms listed out rather than just a formula result.
Reach for it when you want to see the actual numbers instead of plugging values into n/2 × (2a + (n−1)d) by hand, or when you need a quick sanity check that a pattern grows the way you expect. It is handy for verifying a spreadsheet column, generating sample data, or confirming where a geometric series starts to explode versus where it converges in size.
Read the output top-down: the large number is the sum of every term, the Terms field gives the full comma-separated list you can copy, and the three stats show the count, the last term, and the average (sum divided by count). Watch the label on the middle field — it switches to "Common difference (d)" for arithmetic, "Common ratio (r)" for geometric, and "Second term (b)" for Fibonacci-style, so the same box means different things depending on the type you picked.
- For geometric sequences a ratio above 1 grows fast, a ratio between 0 and 1 shrinks toward zero, and a negative ratio alternates sign.
One practical caveat: term count is capped at 1,000, and very large geometric ratios or long Fibonacci runs can overflow into "too large," at which point the sum is no longer a finite number you can trust. Values are also rounded to ten decimal places for display, so treat the last digits of long decimals as approximate rather than exact.
Frequently asked questions
What does the second field mean for a Fibonacci sequence?
For the Fibonacci-style type, the first field is the first term and the second field is the second term. Every term after that is the sum of the previous two, so first term 1 and second term 1 yields 1, 1, 2, 3, 5, 8.
How is the sum calculated?
The calculator adds up every term it generates. This matches the standard closed-form formulas: n/2 * (2a + (n-1)d) for arithmetic and a*(r^n - 1)/(r - 1) for geometric (a*n when the ratio is 1).
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between an arithmetic and a geometric sequence?
In an arithmetic sequence you add the same fixed amount (the common difference) to get each next term, so it grows in a straight line. In a geometric sequence you multiply by the same fixed factor (the common ratio), so it grows or shrinks at an accelerating rate.
How do you find the nth term of an arithmetic sequence?
Use the formula a + (n − 1)d, where a is the first term, d is the common difference, and n is the position you want. For example, the 6th term of a sequence starting at 2 with difference 3 is 2 + 5 × 3 = 17.
What are the first 10 Fibonacci numbers?
Starting from 1 and 1, the first ten are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Each number is the sum of the two before it, and you can change the two starting values to build a Fibonacci-style sequence with a different seed.
Can a geometric sequence have a negative or fractional ratio?
Yes. A fractional ratio between 0 and 1 makes the terms shrink toward zero, and a negative ratio makes the terms alternate between positive and negative values while their size still changes by the same factor each step.
How do you calculate the sum of a sequence?
For arithmetic series the closed form is n/2 × (2a + (n − 1)d), and for geometric series it is a × (rⁿ − 1)/(r − 1) when the ratio is not 1. Both produce the same result as simply adding up every term in the sequence.
What is the average of a number sequence?
The average is the sum of all terms divided by the number of terms. For an arithmetic sequence it equals the midpoint between the first and last term, which is why evenly spaced lists have a tidy average.
Why does my geometric sequence sum say it is too large?
Geometric sequences with a ratio greater than 1 grow exponentially, so a long enough sequence exceeds the range of numbers a browser can represent. Reducing the term count or the ratio keeps the sum within a finite, displayable value.
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