# 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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### Looking for an expansion on the AP sum formula

If I have an x where x starts at x=5, and each step adds 10, so that x1=5, x2=15, x3=25, etc...so that if there were 3 steps the answer would be 5+15+25=45. This is most properly answered by https://...
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### Analytical expression for tetrahedral progression

During my engineering studies we did get some Calculus and Algebra background, but I have a lack of knowledge in other topics such as Combinatorics, Recurrences and Progressions. Therefore I would ...
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### Generalised formula for the given series

I have the below series : (1 * 0) + (2 * 1) + (3 * 2) + (4 * 3) + ... + (n * (n-1)) Is it possible to have a generalised formula for this. Also such series like ...
188 views

### Angles of a triangle - are in a Geometric Progression, possible values for the common ratio other than 1 [closed]

Let us assume that there exists a triangle with measures of its angles in a Geometric Progression (G.P.) with a common ratio other than 1. Then what are the possible ranges of (that is starting set ...
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### "Magic" numbers are those divided by all partial digit sums: prove that there is no infinite set of "magic" powers among the natural powers of $\ell$

For a natural number $n$, let $P_n$ the set of sums of each subset of digits in decimal notation of $n$. A number is magic if for each $s \in P_n$, we have $s \ | \ n$. Let's consider a number $\ell$, ...
1 vote
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### Succession of geometric shapes

A succession of geometric shapes is obtained by dividing squares into smaller squares. The first three geometric shapes of these successions are illustrated as follows in the figure: Considering that ...
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### Possible values of r (common ratio) if r is equal to d (common difference)

The common difference d of an AP is equal to the common ratio r of a GP. I have been told that the sum of the first ten terms of the AP is equal to fifteen times the sum of the first three terms of ...
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### What is the solution to this problem (Geometric and Arithmetic progression)?

Numbers $a , b,c , 64$ are consecutive members of a geometric progression. Numbers $a,b,c$ are respectively the first, fourth, eighth members of an arithmetic progression. Calculate $a + b - c$
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### How to prove that a spiral that I have is logarithmic or archimedean?

I am conducting a research on modelling a spiral.. I know that the shape of the spiral on my pencil shavings is logarithmic indeed, How do i prove that? How do I prove it is logarithmic and not ...
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Find all $a, b$ such that the roots of $x^3 + ax^2 + bx − 8 = 0$ are real and in a geometric progression. I did deduce the answer till $a=\dfrac{-b}{2}$. Using the Vieta's relations I deduced that if $... 1 vote 4 answers 724 views ### Find the sum of$5.5+55.55+555.555..$up till n terms? Find the sum of$5.5+55.55+555.555..$up till n terms? My attempt:$ 5.5+55.55+555.555 ...  5(1.1+11.11+111.111...)  \dfrac{5}{9} \times 9(1.1+11.11+111.111..)  \dfrac{5}{9} (9.9+99.99+999.... 105 views