Geometric Sequence Calculator
Work with geometric sequences — find terms and sums.
Multiplying by the same each step
A geometric sequence multiplies by a constant ratio each step — like 2, 6, 18, 54, multiplying by three each time. This finds any term and the sum of a range, for sequences that grow or shrink by a fixed factor.
Enter the sequence details to find terms or the sum.
Explosive growth and infinite sums
Geometric sequences behave very differently from arithmetic ones. Because they multiply rather than add, a growing geometric sequence explodes — this is exponential growth, the same force behind compound interest and viral spread, where the numbers stay modest then suddenly rocket. But there is a beautiful twist when the ratio is between zero and one, so each term is smaller than the last: the sequence shrinks toward zero, and remarkably, adding infinitely many terms gives a finite total. This is why an unending sum like a half plus a quarter plus an eighth and on forever comes to exactly one. That an infinite process can have a finite answer is one of the genuinely mind-bending results that geometric sequences make concrete.
Frequently asked questions
What makes a sequence geometric?
Each term is multiplied by the same constant ratio — like 2, 6, 18, 54, multiplying by three each time — rather than adding a fixed amount.
Can an infinite geometric sequence have a finite sum?
Yes — when the ratio is between zero and one, the terms shrink toward zero and the infinite sum comes to a finite total, like a half plus a quarter plus an eighth equalling one.
Is anything uploaded?
No. The calculation happens in your browser.