Grade 10 Math lesson

1. MATHEMATICS 10

2. FIBONACCI SEQUENCE

3. FIBONACCI SEQUENCE
The Fibonacci sequence is a series of numbers where each number
is the sum of the two preceding ones. It starts with 0 and 1, and
every subsequent number is the sum of the two preceding ones.
Here are the first few numbers in the Fibonacci sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

4. FIBONACCI SEQUENCE
As you can see, each number is the sum of the two
numbers that came before it. For example, 2 is the
sum of 1 and 1, 3 is the sum of 1 and 2, and so on.
This pattern continues indefinitely.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

5. FIBONACCI SEQUENCE
The Fibonacci sequence has been found to have
numerous mathematical and real-world applications. It
appears in various natural phenomena, such as the
arrangement of leaves on a stem, the branching of trees,
the spirals of shells, and even in the growth patterns of
populations. It also has applications in computer
algorithms, financial markets, and more.

6. HARMONIC SEQUENCE

7. HARMONIC SEQUENCE
A harmonic sequence is a sequence of numbers in which the reciprocal of
each term is in arithmetic progression. In other words, the difference
between the reciprocals of consecutive terms is constant. Here are a few
examples of harmonic sequences:
1.) 1, 1/2, 1/3, 1/4, 1/5, ... In this sequence, each term is the
reciprocal of a positive integer. The reciprocals form an
arithmetic progression, where the common difference is -1.

8. HARMONIC SEQUENCE
2.) 1/2, 1/4, 1/6, 1/8, 1/10, ... In this sequence, each term is the
reciprocal of an even number. Again, the reciprocals form an
arithmetic progression, where the common difference is -1/2.
3.) 3, 1/3, 1/9, 1/27, 1/81, ... In this sequence, each term is
obtained by taking the reciprocal of the corresponding power
of 3. Here, the reciprocals form an arithmetic progression,
with the common difference being -1/3.

9. HARMONIC SEQUENCE
Harmonic sequences have applications in
various areas of mathematics, including series
and sums, calculus, number theory, and
physics. They are also used in music theory,
where harmonic ratios and progressions play a
significant role in understanding chords and
intervals.

10. Worksheet Time!