Meaning of number sequences how to#
Meaning of number sequences series#

This sequence is similar to the square sequence, except that the elements are cubes of numbers. Which is the same as the squares of the numbers 1,2,3, and so on. This type of sequence is obtained by a pattern forming squares. This type of sequence is obtained from elements that form an equilateral triangle.Ĭonsider this sequence as an example, 1,3,6,10,….

Reciprocal of the terms gives you 1, ½, ⅓, ¼, …. Harmonic Sequence:Ī harmonic sequence represents the reciprocal of the terms present in an arithmetic sequence.įor example, 1, 2, 3, 4,…. Geometric Sequence:Ī sequence in which the ratio between the element and the preceding element continues to be constant is a geometric sequence.Īn example of a geometric sequence is 1, 4,16,64,…… The first difference between the number and its preceding numbers is 1, 2, 3, and 4.īut the second difference between elements and their preceding element is 1. In quadratic sequence, the second difference is the same. In an arithmetic sequence, the difference between the preceding elements is the same. Now that you know the arithmetic sequence, you can understand the quadratic sequence. The fixed number added to the preceding number is called the common difference. Arithmetic Sequence:Ī number sequence in which every element is the addition of the previous element with a fixed number is an arithmetic sequence. Read further to know these types of number sequences. Other than these types, there can be other number sequences. There are a few types of number sequences that have a specific pattern. The number of sequences for which the number of elements is not finite, the sequence is said to be an infinite sequence. Here, a is the first term, d is the common difference in arithmetic sequence, r is the ratio in geometric sequence and n is the number of term.Finite sequences are the ones where you can determine the number of elements in the number sequence. We sometimes write a sequence as ( a n ), if it is finite. This means that a sequence is really a special kind of function with natural numbers as its domain.

Meaning of number sequences how to#

The rule should tell us how to get the thing in the n-th place, where n can be any natural number. So another way to write down a sequence is to write a rule for finding the thing in any place one wants. This does not work for an infinite sequence. If a sequence is finite, it is easy to say what it is: one can simply write down all the things in the sequence. This sequence never ends: it starts with 2, 4, 6, and so on, and one can always keep on naming even numbers. An example of a sequence that is infinite is the sequence of all even numbers, bigger than 0. The other kind is infinite sequences, which means that they keep going and never end. For example, (1, 2, 3, 4, 5) is a finite sequence. One kind is finite sequences, which have an end.

Sequences made up of numbers are also called progressions. For example, both (Blue, Red, Yellow) and (Yellow, Blue, Red) are sequences, but they are not the same.

The order that the things are in matters. In maths, a sequence is made up of several things put together, one after the other.

Meaning of number sequences series#

In ordinary use, it means a series of events, one following another. It is used in mathematics and other disciplines. A sequence is a word meaning 'a set of related events, movements or items that follow each other in a particular order'.