Page 10 - Math 21 Module_Chapter One

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How did you determine your answers to the
task?____________________________________________________________________________
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READ: Read and study the following concepts

A pattern includes a repeated or recurring design. It is either natural or
human-made. Patterns are everywhere and are encountered everyday - from
the layout of the floor tiles, the design of fabrics/textiles, the blocks played by
kids, the arm and leg movements in an exercise, to the arrangement of books
in a library. Studying patterns helps people identify the relationships and logical
connections of things that would allow them to generalize or predict events.

For any patterns, it is necessary to try to analyse what is happening
before you can predict the next number, or the pattern. Perhaps, you were
able to answer the first task by looking at some patterns.

Number Patterns

Generally, patterns in numbers are sequence in a given set or series of
numbers. The pattern usually establishes a common relationship among all the
numbers in the set. In Mathematics, a basic and common number pattern is
called a sequence. The numbers in the sequence are called the term; that is,
the first number is the first term, the second number is the second term and so
on. In predicting a number pattern, at least 4 or 5 numbers are provided as
basis; otherwise, the predicted pattern may not hold for all the numbers under
consideration.

There are many interesting number patterns in Mathematics. The
common mathematical sequences are the arithmetic sequence and the
geometric sequence. Other number patterns include triangular numbers,
square numbers, cube numbers, pentagonal numbers, and others. Aside from
arithmetic and geometric sequences, a special number pattern to be
discussed in this chapter is the Fibonacci sequence.

Sequences in Mathematics

1. Arithmetic Sequence - is a sequence of numbers in which the
difference between any two consecutive numbers or expressions is the same.

Example1.1.1
a. 2, 4, 6, 8, 10
b. 5, 10, 15, 20, 25