Geometric Sequence Calculator
List every term, find the Nth term, and compute the sum of a geometric sequence from its first term and common ratio — runs 100% in your browser with no upload.
2, 6, 18, 54
54
80
🔒 Calculated in your browser — nothing is uploaded.
What this geometric sequence calculator does
Enter the first term, the common ratio, and how many terms you want, and this tool instantly lists the whole sequence, highlights the Nth (last) term, and adds everything up into a total. A geometric sequence is any list of numbers where each term is found by multiplying the one before it by the same fixed number — the common ratio — such as 2, 6, 18, 54, where the ratio is 3. The ratio can be greater than one for a growing sequence, between zero and one for a shrinking one, or negative to make the signs alternate, and both the first term and the ratio may be decimals.
The formulas behind the results
The Nth term is computed directly with a₁ × r^(N − 1), so you get the value of the last term without stepping through every multiplication. The sum uses the closed-form series formula a₁ × (r^N − 1) / (r − 1); when the ratio is exactly 1 every term is the same, so the sum is simply a₁ × N, which the tool handles as a special case to avoid dividing by zero. Everything recalculates live as you type, and each result has its own copy button. To keep the listing readable and responsive, the number of terms is limited to 1000.
Frequently asked questions
How is the Nth term different from the sum?
The Nth term is the value of a single term — the last one in your list — found with a₁ × r^(N − 1). The sum adds every term together, from the first up to the Nth, using the series formula a₁ × (r^N − 1) / (r − 1).
Can the common ratio be negative, a fraction, or exactly one?
Yes. A negative ratio makes the signs alternate, a ratio between 0 and 1 makes the sequence shrink toward zero, and a ratio of exactly 1 repeats the first term so the sum becomes first term × N.
What is the 'sum to infinity'?
When the common ratio is between −1 and 1 (|r| < 1) the terms shrink toward zero and the series converges to a finite total even with infinitely many terms: a₁ / (1 − r). The tool shows this 'Sum to ∞' row only in that case — for a ratio of 1/2 starting at 1, it equals 2. When |r| ≥ 1 the series diverges, so the row is hidden.
Is anything I enter uploaded to a server?
No. Every calculation runs entirely in your browser using JavaScript. The numbers you type are never sent, stored, or logged anywhere.