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The descending 5-6 sequences, also known as descending third sequences, consist of a series of chords whose root notes descend by a third each sequential repetition. [8] The basic pattern of a descending 5-6 sequence (with intervening chords removed) in C major. The pattern in the lower staff descends by a third each time in this sequence. Play ⓘ
GCSE Bitesize was launched in January 1998, covering seven subjects. For each subject, a one- or two-hour long TV programme would be broadcast overnight in the BBC Learning Zone block, and supporting material was available in books and on the BBC website. At the time, only around 9% of UK households had access to the internet at home.
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is
Counting the different patterns of successive L and S with a given total duration results in the Fibonacci numbers: the number of patterns of duration m units is F m+1. [5] Knowledge of the Fibonacci sequence was expressed as early as Pingala (c. 450 BC–200 BC).
The same sequence of shapes, converging to the Sierpiński triangle, can alternatively be generated by the following steps: Start with any triangle in a plane (any closed, bounded region in the plane will actually work). The canonical Sierpiński triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image).
Other versions of the pea pattern are also possible; for example, instead of reading the digits as they first appear, one could read them in ascending order instead (sequence A005151 in the OEIS). In this case, the term following 21 would be 1112 ("one 1, one 2") and the term following 3112 would be 211213 ("two 1s, one 2 and one 3").
Suffix trees are often used in bioinformatics applications, searching for patterns in DNA or protein sequences (which can be viewed as long strings of characters). The ability to search efficiently with mismatches might be considered their greatest strength.
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).