A geometric progression is a list of numbers where each term is found by multiplying the previous one by the same constant. This constant is called the common ratio. Geometric progressions appear in both mathematical theory and real-world situations involving repeated growth or decay.
The general form of a geometric progression is:
a, ar, ar², ar³, …
where a is the first term and r is the common ratio.
A geometric progression can grow or shrink:
- If the common ratio is greater than 1, the terms increase.
- If it’s between 0 and 1, the terms decrease.
- If the ratio is negative, the terms alternate in sign.
Geometric progression is often used interchangeably with geometric sequence, and the terms mean the same thing. Both refer to a sequence of numbers with a consistent multiplicative pattern. However, “geometric progression” is more common in older or more formal mathematical texts.
For example, the list 5, 10, 20, 40, 80 is a geometric progression with a first term of 5 and a common ratio of 2. Each term is double the one before it.
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