# Questions tagged [geometric-progressions]

A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence

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### G.P. geometry relation

By means of a single geometrical diagram, can you show why a geometrical progression is called a geometrical progression? I have thought about showing consecutive diagrams of square areas to either ...
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### $\frac{a}{x},\frac{b}{y},\frac{c}{z}$ are in HP

If non-zero numbers $a,b,c,x,y$ and $z$ are such that $a,b,c$ are in AP, $x,y,z$ are in GP and $\frac{a}{x},\frac{b}{y},\frac{c}{z}$ are in HP then prove $|a|=|c|$. I have been trying to solve this ...
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### Write the geometric progression equation

There is a sequence whose elements have the following dependency a[i] = (a[i-1] + 2 * a[i-1] * Sqrt(2)) / 2 a[i=1] = 10 I need to write a sequence equation and ...
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### Running a Ponzi (game theory).

Let's say I'm organizing a transparent Ponzi scheme for gambling purposes. It's a game of doubles. Each player's goal is to double their deposit. Each new entree pays for the players before him in ...
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### Sum of geometric progression [closed]

Given a geometric sequence whose sum of the first ten terms is 4, and whose sum from the 11th to the 30th term is 48. Find the sum the 31st to the 60th term.
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### Prove that $0.\overline{123} = 0.123123123123...$ is rational [closed]

How are we to go about proving that $0.\overline{123} = 0.123123123123...$ can be expressed in the form $\frac{p}{q}$ where $p,q \in \mathbb{Z}$, i.e is rational? Is this to be done using arithmetic ...
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### Finding the area of a fractal with geometric sequences.

Construct an infinite fractal. Stage 0 is a unit square. At each stage, a square is appended to the vertices of the previous stage such that the sides are 1/2 the sides of the previous stage and ...
1 vote
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### What properties does a radix in the context of ISO/IEC 7064 pure check digit system require?

ISO/IEC 7064:2003 defines so-called pure check digit systems. The term “pure” refers to only requiring one modulus as opposed to two moduli (p. 2). A character string satisfies the check of a pure ...
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### Determine the sum value of the first terms of that sequence.

Consider a geometric progression in which the common ratio is a non-zero natural number, knowing that the logarithm of the nth term at the base equal to the common ratio of the sequence is equal to ...
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1 vote
Let $\alpha$ and $\beta$ be the complex roots of $z^3 =1$. Show that the sum of the first $n$ terms in the series $1 + \alpha + \alpha^2 +...$ is either $0, 1$ or $-\alpha^2$ depending on the ...