Geometric Sequence Calculator

How the ratio drives the pattern

In a geometric sequence, each new term is found by multiplying the previous term by the same ratio $r$ .

That makes the nth term formula $a_n = a_1 r^{n-1}$ , which is why even small ratio changes quickly reshape the preview bars.

Use the term list to check whether the sequence is growing, shrinking, or alternating sign.

Checking compound growth patterns and repeated percentage multipliers.
Finding a later term without writing the full list by hand.
Comparing how ratios like $2$ , $rac{1}{2}$ , or $-3$ change the sequence shape.

Calculate arithmetic sequence terms and sums with a staged workflow, compact term preview, and formula board for nth-term reasoning.

Easily calculate the sum of arithmetic and geometric series with our interactive online tool.

Switch between arithmetic, geometric, Fibonacci, prime, square, cube, triangular, and powers-of-two sequences with a compact interactive explorer.