Patterns - UNL Math Department
... Definition: A function f whose domain is N (the Natural Numbers) is called an infinite sequence and its range is Rf = {f(n) | n N } . The notation for sequences is usually written in the form a1 , a2 , a3 , , an , where f (n) an for n N. Sometimes it is more useful to start the “indexing” of v ...
... Definition: A function f whose domain is N (the Natural Numbers) is called an infinite sequence and its range is Rf = {f(n) | n N } . The notation for sequences is usually written in the form a1 , a2 , a3 , , an , where f (n) an for n N. Sometimes it is more useful to start the “indexing” of v ...
B3 Number Sequences Activities
... Then multiply the fifth and sixth terms. What do you notice? Now square and add the first six numbers and multiply the 6th and 7th numbers. Generalise your results. ...
... Then multiply the fifth and sixth terms. What do you notice? Now square and add the first six numbers and multiply the 6th and 7th numbers. Generalise your results. ...
Patterns and Sequences
... Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add the integer (-3) to each term. The next three terms are: ...
... Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add the integer (-3) to each term. The next three terms are: ...
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.