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Geometric Progression (GP)

Explore the concept of geometric progressions and their formulas, including how to calculate terms and sums for finite and infinite sequences. Understand the role of the common ratio and first term, and prepare to apply these concepts in competitive programming challenges.

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Geometric progression is a sequence of numbers such that each term after the first is obtained by multiplying the previous one by a fixed non-zero number, called the common ratio. For example:

3,6,12,24,...3, 6, 12, 24, ...

Here the first term, aa, is 33, a=3a=3, and the common ratio, rr, is 22, r=2r=2.

In general,

a,ar,ar2,ar3,...,arn1a, ar, ar^2, ar^3, ... , ar^{n-1} ...