Definition of Ratio of a geometrical progression. Meaning of Ratio of a geometrical progression. Synonyms of Ratio of a geometrical progression

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Definition of Ratio of a geometrical progression

Ratio of a geometrical progression
Ratio Ra"ti*o, n. [L., fr. reri, ratus, to reckon, believe, think, judge. See Reason.] 1. (Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b by a/b; or (less commonly) the second is made the dividend; as, a:b = b/a. Note: Some writers consider ratio as the quotient itself, making ratio equivalent to a number. The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule. 2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress. Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

Meaning of Ratio of a geometrical progression from wikipedia

- one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly...
- In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant...
- golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities ⁠ a {\displaystyle...
- techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and...
- mathematical sequence known as a geometric progression may also be used in positional voting. Here, there is instead a common ratio r between adjacent weightings...
- A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi...
- various units of measurement. An early expression of ratio scale was articulated geometrically by Eudoxus: "it was ... in geometrical language that the...
- Sequences that have the property that the ratios of consecutive terms are equal are called geometric progressions. Definitions 9 and 10 apply this, saying...
- is a right triangle whose sides are in geometric progression. If the sides are formed from the geometric progression a, ar, ar2 then its common ratio r...
- arithmetico-geometric sequence is the result of element-by-element multiplication of the elements of a geometric progression with the corresponding elements of an...