A geometric progression is a series where each term is found by multiplying the previous term by a fixed number called the common ratio. The nth term is given by anrn-1 and the sum of the first n terms is given by (1-rn)/(1-r). Key formulas are provided to calculate individual terms and the partial sum using the first term a, common ratio r, and number of terms n. Examples demonstrate applying the formulas to find terms, partial sums, common ratios, and first terms for a variety of geometric series.