Geometric Sequence Calculator

Comprehensive Guide

A geometric sequence changes by multiplying by a constant ratio each step. That makes it the natural opposite of an arithmetic sequence. The calculator is useful whenever growth or decay happens by repeated multiplication rather than repeated addition.

Compound interest, bacteria growth, and depreciation are all geometric patterns in disguise. If the ratio is greater than 1, the sequence grows; if it is between 0 and 1, the sequence shrinks. The calculator shows both the nth term and the accumulated sum when that sum is defined.

Real-World Examples

A sequence starting at 2 with ratio 3 becomes 2, 6, 18, 54, and so on. The 5th term is 162 and the sum of the first five terms is 242. If the ratio changes from 3 to 2, the numbers stay much smaller.

Because each step multiplies, the values can get large quickly. That is why a geometric calculator is useful for spotting growth before it gets out of hand.

Reference Table

Frequently Asked Questions