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Sequences as Functions Learning Task
... The first six sequences above are finite sequences, because they contain a finite number of terms. The last three are infinite sequences because they contain an infinite number of terms. The three dots, called ellipses, indicate that some of the terms are missing. Ellipses are necessary for infinit ...
... The first six sequences above are finite sequences, because they contain a finite number of terms. The last three are infinite sequences because they contain an infinite number of terms. The three dots, called ellipses, indicate that some of the terms are missing. Ellipses are necessary for infinit ...
A10 Generating sequences
... The position-to-term rule for a sequence is very useful because it allows us to work out any term in the sequence without having to work out any other terms. We can use algebraic shorthand to do this. We call the first term T(1), for Term number 1, we call the second term T(2), we call the third ter ...
... The position-to-term rule for a sequence is very useful because it allows us to work out any term in the sequence without having to work out any other terms. We can use algebraic shorthand to do this. We call the first term T(1), for Term number 1, we call the second term T(2), we call the third ter ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.