#MathsInMinutes Day 46: Geometric progressions

#MathsInMinutes Day 46: Geometric progressions

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#MathsInMinutes Day 46: Geometric progressions

A geometric progressions is an ordered list of numbers of numbers in which each successive term is the product of the previous term and a constant number. An example is 1, 4, 16, 64, 256, … where the constant multiplying factor, known as the common ratio r, is 4.

The partial sum of a geometric progression is

Sn = a + ar + ar² + … + ar^n

If the modulus r is greater than 1 then this diverges to plus or minus infinity, but if the modulus is less than 1, then the limiting series, called a geometric series, tends to the limit

S = a / (1 – r)

Geometric progressions arise in many mathematical problems, and are fundamental to the study of compound interest and value in accountancy. Many mathematicians would argue that they also resolve Zenos paradox, since the sums of the distances covered and time taken be the hare are geometric progressions that sum to the distance of the race.

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