Write the expression of the geometric progression with applications.
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Geometric sequences (with common ratio not equal to −1−1, 11 or 00) show exponential growth or exponential decay, as opposed to the linear growth (or decline) of an arithmetic progression such as 4,15,26,37,48,⋯4,15,26,37,48,⋯ (with common difference 1111). This result was taken by T.R. Malthus as the mathematical foundation of his Principle of Population. Note that the two kinds of progression are related: exponentiating each term of an arithmetic progression yields a geometric progression, while taking the logarithm of each term in a geometric progression with a positive common ratio yields an arithmetic progression.
An interesting result of the definition of a geometric progression is that for any value of the common ratio, any three consecutive terms aa, bb, and cc will satisfy the following equation:
b2=ac
An interesting result of the definition of a geometric progression is that for any value of the common ratio, any three consecutive terms aa, bb, and cc will satisfy the following equation:
b2=ac
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