geometric progression
geometric progression — noun
1. a sequence created through repeated multiplication by the same value: starting f
a sequence created through repeated multiplication by the same value: starting from an initial number, you keep multiplying by a fixed quantity (the common ratio) to get the next number — for example, 2, 6, 18, 54, … or 1, 3, 9, 27, 81, …
The teacher asked the class to find the next term in the geometric progression 5, 15, 45, 135.
finding the next term in a given GP
Li Wei saw that a geometric progression grows fast when the common ratio exceeds one.
common ratio determines growth speed
In the geometric progression 64, 32, 16, 8, each term is half of the one before it.
Aicha saw that the numbers in the table formed a geometric progression with a 1.5 ratio.
Students calculated the sum of the first eight terms of a geometric progression starting with 3.
- geometric sequence
exactly the same meaning; 'sequence' and 'progression' are interchangeable in mathematics
- geometric series
often used for the sum of the terms of a geometric progression, though some textbooks use it interchangeably
- arithmetic progression
a sequence where each term differs by a constant ADDITION or subtraction, not multiplication
用法筆記
A geometric progression has a constant multiplier (common ratio) between consecutive terms. This distinguishes it from an arithmetic progression, where the difference between terms is constant.