Ever noticed patterns in numbers that just seem to… grow exponentially? You might be witnessing a geometric progression (GP) in action! In simple terms, a GP is a sequence where each term is found by multiplying the previous term by a constant value, called the common ratio. Think of it like compound interest – your initial amount grows by the same percentage each period.
Imagine a single cell dividing. Then those two cells divide, and so on. That's a GP! Or think about bouncing a ball; each bounce is a fraction of the height of the previous bounce.
The general formula for a GP is a, ar, ar², ar³, and so on, where 'a' is the first term and 'r' is the common ratio. Understanding GPs unlocks powerful tools for modeling growth, decay, and many other real-world phenomena. So next time you see a pattern of multiplicative growth, remember the magic of geometric progressions!
