Geometric progressions: the nth term, the sum of n terms and the sum to infinity, the geometric mean, and the relation between the arithmetic and geometric means.
3 lessons, about 1 h 15 min3 simulations12 problems3 practice questionsPython in every lesson
Created by StemPy LabA geometric progression (GP) is a sequence in which each term is the one before times a fixed number , the common ratio. Its nth term is . Three terms , , are in GP when . Growth or decay by a fixed percentage, like compound interest, makes a GP.
The sum of the first terms of a GP is , or when . When the terms shrink fast enough for the sums to settle at . This turns recurring decimals into fractions and adds up endless bounces.
The geometric mean of two positive numbers and is , and inserting means between them makes a GP of terms. The arithmetic mean is never less than , and the two are equal only when . This AM-GM inequality finds least and greatest values.
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