Sequences and Series
Geometric Series
A GEOMETRIC SERIES is the sum of the terms of a geometric sequence. Copy and paste the following link into your browser to learn more about solving geometric sequences and series: https://youtu.be/THV2Wsf8hro
Summation Notation
A simple method for indicating the sum of a finite (ending) number of terms in a sequence is the SUMMATION NOTATION. This involves the Greek letter sigma, Σ. When using the sigma notation, the variable defined below the Σ is called the INDEX OF SUMMATION. The lower number is the lower limit of the index (the term where the summation starts), and the upper number is the upper limit of the summation (the term where the summation ends). Copy and paste the following link into your browser to learn more about using summation notation: https://youtu.be/De_Eml90GbU
Arithmetic Series
An ARITHMETIC SERIES is the sum of the terms of an arithmetic sequence. Copy and paste the following link into your browser to learn more about solving arithmetic series: http://www.bing.com/videos/search?q=solving+arithmetic+series&&view=detail&mid=EFC84EFD6A6116E98754EFC84EFD6A6116E98754&FORM=VRDGAR
Geometric Sequence
GEOMETRIC SEQUENCE is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is ▶︎▶︎ a[subscript n] = a₁ rⁿ - 1 The value 'r' is called the COMMON RATIO. It is found by taking any term in the sequence and dividing it by its preceding term. Copy and paste the following link into your browser to learn more about solving geometric sequences: http://www.bing.com/videos/search?q=Geometric+Sequence&&view=detail&mid=1ECBF78C06390BF3AA551ECBF78C06390BF3AA55&FORM=VRDGAR
Sequences: Definitions
In algebra, a SEQUENCE is an enumerated 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 either the set of the natural numbers (for infinite sequences) or the set of the first n natural numbers (for a sequence of finite length n). The position of an element in a sequence is its RANK or INDEX; it is the integer from which the element is the IMAGE. It depends on the context or of a specific convention if the first element has index 0 or 1. When a symbol has been chosen for denoting a sequence, the NTH ELEMENT of the sequence is denoted by this symbol with n as a superscript [ⁿ]; for example, the nth element of the Fibonacci sequence is generally denoted Fⁿ.
Arithmetic Sequence
In mathematics, an arithmetic progression (AP) or ARITHMETIC SEQUENCE is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 ... is an arithmetic progression [sequence] with COMMON DIFFERENCE of 2. Copy and paste the following link into your browser to learn more about solving arithmetic sequences: https://youtu.be/lj_X9JVSF8k
Sequences: Examples
Shown below are examples of sequences: ▶︎▶︎ 1, 3, 5, 7, 9... ▶︎▶︎ -8, 3, 14, 25... ▶︎▶︎ 1, 2, 4, 8, 16... The three dots mean to continue forward in the pattern established. Each number in the sequence is called a TERM. In the sequence 1, 3, 5, 7, 9, ..., 1 is the first term, 3 is the second term, 5 is the third term, and so on. The notation a¹, a², a³,... aⁿ is used to denote the different terms in a sequence into infinity.
