A sequence of real numbers \((\alpha_n)_{n\in\mathbb N}\) is called a geometric progression (or a continued proportion), if its sequence members can be built recursively by \[\begin{array}{rcl}\alpha_0&:=&\alpha\\\alpha_n&:=&\alpha\beta^n\end{array}\] for some fixed real numbers \(\alpha,\beta\) with \(\beta\neq 0\). Thus the sequence is given by \(\alpha,\alpha\beta,\alpha\beta^2,\alpha\beta^3\ldots\).
The number \(\beta\) is called the common ratio or scale factor.
Corollaries: 1 2
Definitions: 3
Proofs: 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Propositions: 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
Sections: 63
Topics: 64
