Geometric Progressions — O/L Mathematics

A Geometric Progression (GP) is a sequence of numbers where each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. This is the defining property that distinguishes a GP from other sequences like arithmetic progressions.

For example, the sequence 2, 6, 18, 54, ... is a GP because each term is multiplied by 3 to get the next term. The common ratio here is 3. Similarly, 100, 50, 25, 12.5, ... is a GP with common ratio 1/2.

The general form of a GP is: a, ar, ar², ar³, ar⁴, ...

Here: a represents the first term of the progression. r represents the common ratio (the multiplier).

The common ratio r can be found by dividing any term by its preceding term. That is, r = (second term) / (first term) = (third term) / (second term), and so on. For a valid GP, this ratio must be constant throughout the sequence.