Week 6 Fibonacci and Harmonic Sequence.pptx

Fibonacci and Harmonic Sequence  OBJECTIVES: Illustrate the Fibonacci sequence. Illustrate the Harmonic sequence. Solve problems involving Fibonacci and harmonic sequence.  FIBONACCI SEQUENCE The pattern shows that each successive term is the sum of the two preceding...

Fibonacci and Harmonic Sequence  OBJECTIVES: Illustrate the Fibonacci sequence. Illustrate the Harmonic sequence. Solve problems involving Fibonacci and harmonic sequence.  FIBONACCI SEQUENCE The pattern shows that each successive term is the sum of the two preceding terms. This sequence was later named after Leonardo Fibonacci.  FIBONACCI SEQUENCE The Fibonacci Sequence is defined by the recursive formula = + with = = 1  Example: Give the recursive formula for the Fibonacci sequence = + , find the following: a + + + =1+1 =2  HARMONIC SEQUENCE Harmonic sequence is a special type of sequence in which the reciprocal of each term forms an arithmetic sequence.  HARMONIC SEQUENCE A sequence of the form , , , …, is a harmonic sequence, where is the first term, d is the common difference and n is the number of terms.  Example: Find the 8th term of the harmonic sequence , , ,…, = = = = = 1 𝑇 h𝑢𝑠 𝑡h𝑒 8𝑡h 𝑡𝑒𝑟𝑚 𝑜𝑓 𝑡h𝑒 h𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒 𝑖𝑠 4  HARMONIC MEANS Harmonic means are terms between two terms of a harmonic sequence.  Example: Insert the harmonic means between. Make the corresponding arithmetic sequence -2, _, _, _,18. = -2, =18 Solve for the d, we have : = = = Class Agenda: September 1- 5Monday Tuesday Wednesday Thursday Friday Wednesday, September 3 To Do Vocabulary Writing Prompt  Thursday, September 4 Objective Lit Circles Homework  Friday, September 5 Schedule Objective Grammar Skill Weekly Reflection Teacher Resources