A geometric progression is a sequence where each term after the first is obtained by multiplying the preceding term by a constant ratio. The sequence is defined by a starting value and a common ratio used to calculate subsequent terms. For example, in the sequence 1, 3, 9, 27, 81, each term after the first is found by multiplying the prior term by 3, making 3 the common ratio. The general formula for a geometric sequence is a, ar, ar^2, ar^3, where a is the first term and r is the common ratio used to exponentiate subsequent terms.