geometric sequence

A geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, 1, 1/2, 1/4, 1/8 is a geometric sequence with a common ratio of 1/2.12

A geometric series is the sum of the terms in a geometric sequence. If the absolute value of the common ratio is less than 1, the geometric series converges to a finite sum. This concept was challenging for ancient mathematicians, but the development of analysis and limits in the 18th century helped clarify how an infinite series can yield a finite sum.32