A PPT Presentation for Type of Sequence: Harmonic and Fibonacci Sequence

1. HARMONIC & FIBONACCI
SEQUENCE
INSPIRED BY
LESSON 9

2. GEOMETRIC
SERIES
Learning Outcomes
• Define Harmonic and Fibonacci
Sequence
• Solve problems involving Harmonic and
Fibonacci Sequence
• Identify sequence that are geometric.

3. HARMONIC SEQUENCE
– is a sequence such that the reciprocals of terms forms
an arithmetic sequence.
…
… is a HARMONIC SEQUENCE

4. Solution:
Step 1: Find the reciprocals of each term
Is the sequence ,
Example 1:
Step 2: Check if the reciprocal forms an
Arithmetic Sequence

5. Solution:
Step 1: Continue the Arithmetic Sequence to
form the first 8 terms
Given the Arithmetic Sequence -20, -26, -32, -
38…Find the first 8 terms of its Harmonic
Sequence
Example 2:
Step 2: Find the reciprocals of each term to form the
first 8 terms of the corresponding Harmonic Sequence.

6. FIBONACCI SEQUENCE
– is a sequence where its first two terms
are either both 1 or 0 and 1, and each term
therefore is obtained by the two preceding
terms

7. Solution:
What is the next five terms of the sequence
1, 1, 2, 3, 5, ___, ___, ___, ___, ____
Example 3:
1, 1, 2, 3, 5, ___, ___, ___, ___, ____
8 13 21 34 55

8. QUIZ NO. 11
DIRECTION: Give what is asked for each
number.
2.¿ 𝐼𝑛 h
𝑡 𝑒 𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒−
4
5
,−4 ,
4
3
,,.. h
𝑤 𝑎𝑡 𝑖𝑠 h
𝑡 𝑒8 h
𝑡 𝑡𝑒𝑟𝑚?