fibonacci and harmonic sequence grade 10.pptx

other sequences (fibonacci and harmonic)

1. Other Sequences ( Fibonacci, Harmonic,…) MARK O. AGUSTIN, LPT MATHEMATICS TEACHER

2. OBJECTIVES Illustrate other types of sequences; Solve problems involving sequences.

3. Fibonacci Sequence

4. FIBONACCI In 1202, Leonardo of Pisa, who was called Fibonacci, wrote a book on arithmetic and algebra titled Liber Abaci . The sequence 1 1 2 3 5 8 13 … LEONARDO OF PISA

5. FIBONACCI SEQUENCE The sequence 1 1 2 3 5 8 13 … Is called the Fibonacci Sequence. The first two terms of this sequence are 1 and each successive term is the sum of the preceding terms. Add more information here as needed

6. GENERAL TERM OF FIBONACCI- TYPE SEQUENCE A Fibonacci type sequence is a sequence in which the general term is given by the formula Where and are given. The Fibonacci sequence corresponds to = =1   GOLDEN RATIOS

7. EXAMPLE If and represent any first numbers, list the first eight terms of this Fibonacci type sequence. Given and . Find . Find the 30 th term of the Fibonacci sequence  

8. Harmonic Sequence

9. Harmonic Sequence If are terms of an arithmetic sequence, then the sequence of the reciprocals of these terms, , is called a harmonic sequence.   FIRST MEMBER OF HARMONIC SEQUENCE

10. EXAMPLE The sixth term of the harmonic sequence . The first term of a harmonic sequence whose fourth term is and whose twelfth term is