In a city of over one million people, the East Side is home to predominately Latinos, with African Americans, Vietnamese, Filipinos, Cambodians, and Samoans making up smaller, but still significant ethnic populations. Those of us who live and work in and around the neighborhood of Overfelt, commonly refer to Overfelt as being located in the East Side of San Jose. When people hear of San Jose, they tend to think of Silicon Valley, high tech, and astronomical housing prices. Overfelt High School is located in San Jose, California. Overall, this unit serves as a supplement to enhance my existing textbook resources, to better support students in any course that works with linear, quadratic, and exponential sequences and functions. In addition to tabular models, geometric representations of sequences will be used as an alternative approach to represent sequences, leading to algebraic representations. This unit will look at how the common difference, second difference, or common ratio between consecutive terms of a sequence can be used to determine a sequence’s recursive and explicit equations. In textbooks, formulas are frequently just given to students based on specific types of sequences. Many of my students are able to observe patterns represented in the sequences, but struggle in taking those observations and translate translating them into algebraic representations. Note that some texts may use the term rule in place of equation. They are also asked to identify key characteristics of the sequence, and to use these to write both recursive equations and explicit equations for a n, the nth term in the sequence. When given a few terms in a sequence, students are expected to classify the sequence type, as being potentially one of the three special ones, or “other”. This curriculum unit discusses each of these three types in the sections below. Many potentially infinite sequences are formed according to simple rules, and such sequences are also often referred to as “patterns”.Īt the high school level, students are introduced to three main special types of sequences: arithmetic (linear), geometric (exponential), and quadratic. For example, the sequence 2,4,6,8,10 is a finite sequence with five terms, while 2,4,6,8,10,… is an infinite sequence.

Infinite sequences do not stop and are assumed to continue indefinitely. Finite sequences, are sequences that stop after a certain number of terms. Each number in a sequence is called a term. In mathematics, a sequence is defined as an ordered list of numbers. Sequencing Math DNA: Differences, Nth Terms, and Algebraic Sequences by Lawrence E.

Sequences algebra