Sequences
... and is denoted by a symbol such as bn. The sequence whose n-th term is bn is denoted {bn}. ...
... and is denoted by a symbol such as bn. The sequence whose n-th term is bn is denoted {bn}. ...
Year 10 Sheet 13
... The number of balls needed to build each tower forms a sequence called triangular numbers. The formula for calculating the nth term of a triangular number is: ...
... The number of balls needed to build each tower forms a sequence called triangular numbers. The formula for calculating the nth term of a triangular number is: ...
lecture notes 5
... 4. (MathCounts 2006) A dresser has five drawers stacked vertically. To be able to reach the contents in an open drawer, no drawer that is adjacent to the open drawer may be open at the same time. In how many ways can one or more drawers be open so that the contents in each of the open drawers can be ...
... 4. (MathCounts 2006) A dresser has five drawers stacked vertically. To be able to reach the contents in an open drawer, no drawer that is adjacent to the open drawer may be open at the same time. In how many ways can one or more drawers be open so that the contents in each of the open drawers can be ...
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.