Problem Solving with Patterns

This presentation presents three common sequences-the Arithmetic sequence, the Geometric sequence and the Fibonacci sequence.

1. Problem Solving with Patterns

2. What is a Pattern? A pattern constitutes a set of numbers or objects in which all members are related with each other by a specific rule. Pattern is also known as sequence. What is a Sequence? A sequence is a succession of numbers in a specific order. Each number in a sequence is called term . The terms are formed according to some fixed rule or property. They are arranged as the first term, second term, third term, and so on.

3. FINITE AND INFINITE SEQUENC E A sequence with a definite number of terms is a finite sequence while a sequence with no definite number of terms is an infinite sequence. ARITHMETIC SEQUENCE Arithmetic Sequence is a sequence where every term after the first is obtained by adding a constant called common difference. Common Difference is a constant added to each term of an arithmetic sequence to obtain the next term.

4. GEOMETRIC SEQUENCE Geometric Sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio (r). Common Ratio (r) is a constant multiplied to each term of a geometric sequence to obtain the next term of the sequence.

5. THE FIBONACCI SEQUENCE Leonardo of Pisa, also known as Fibonacci (c. 1170–1250), is one of the best-known mathematicians of medieval Europe. In 1202, after a trip that took him to several Arab and Eastern countries, Fibonacci wrote the book Liber Abaci . In this book, Fibonacci explained why the Hindu-Arabic numeration system that he had learned about during his travels was a more sophisticated and efficient system than the Roman numeration system. This book also contains a problem created by Fibonacci that concerns the birth rate of rabbits. Here is a statement of Fibonacci’s rabbit problem. At the beginning of a month, you are given a pair of newborn rabbits. After a month the rabbits have produced no offspring; however, every month thereafter, the pair of rabbits produces another pair of rabbits. The offspring reproduce in exactly the same manner. If none of the rabbits dies, how many pairs of rabbits will there be at the start of each succeeding month?

6. Reference Aufman RF., Lockwood JS., Nation RD., Clegg DK., Mathematical Excursions. Fourth Ed., Cengage Learning © 2018 Capsulized Sef -Learning Empowerment Toolkit ( CapSLET ). Grade 10 Mathematics. Module 1-5.