1. The document describes four types of sequences: arithmetic, geometric, harmonic, and Fibonacci. 2. It provides examples of each type of sequence and how subsequent terms are calculated. For arithmetic sequences each term is obtained by adding a constant, for geometric sequences each term is obtained by multiplying a constant, and for harmonic sequences the reciprocals of the terms form an arithmetic sequence. 3. A Fibonacci sequence is defined as starting with two terms that are either both 1 or 0 and 1, with each subsequent term calculated by adding the two preceding terms.

1. Arithmetic
Geometric
Harmonic
Fibonacci
Sequences

2. How Well do you Know
Me? Determine whether
each sequence is
arithmetic, geometric, or
harmonic. Then, give the
next term of each
sequence.
10
seconds

3. 1
6, 18,
54,
162, ...
Geometric 486
Answer

4. 2
4, 10,
16, 22,
...
Arithmetic 28
Answer

5. 3
625,
125,
25, 5,
Geometric 1
Answer

6. 4
1
2
,
1
4
,
1
6
,
1
8
,…
HARMONIC 1/10
Answer

7. 5
1
3
,
1
6
,
1
9
,
1
12
,…
HARMONIC 1/15
Answer

8. Determine the
next term of the
given sequence
10
seconds

9. 1
1, 1, 2, 3,
5, 8, 13,
21…
34
Answer

10. 2
8, 13,
21, 34,
55,…
89
Answer

11. What kind of
sequence were
given?

12. How did you
obtain the next
term of each
sequence?

13. 1.What is a Fibonacci
sequence?
2. How do you distinguish
them from other types of
sequence?

14. A Fibonacci sequence is a
sequence where its first two
terms are either both 1, or 0 and
1; and each term, thereafter, is
obtained by adding the two
preceding terms.
Example:
0, 1, 1,
2, 3,
5, …

15. Given the
Fibonacci sequence
5, 8, 13, 21, 34, ...
Find the next 6
terms.
55,89,144,233,377,610
Answer

16. If F1 = 6 and F2 =
3, list the first 8
terms of this type
of Fibonacci
sequence.
6,3,9,12,21,33,54,87
Answer

17. Determine whether each
sequence is Arithmetic,
Geometric, Harmonic or
Fibonacci. Then, give the
next term of each sequence.
10
seconds

18. 1
5, 8, 13, 21,
34, …
55- Fibonacci
Answer

19. 2
-1296, 216, -
36, 6,…
-1-Geometric
Answer

20. 3
8.2, 8, 7.8,
7.6, …
7.4-Arithmetic
Answer

21. 4
-1/42, -1/35,
-1/28, -1/21, …
-1/14-Harmonic
Answer

22. 5
2, 9, 16,
23,…
30 -Arithmetic
Answer

23. Arithmetic Sequence is a
sequence where each term
after the first is obtained by
adding a constant called
common difference.
Example:
3,7,11
,15,…

24. Geometric Sequence is a
sequence where each
term after the first is
obtained by multiplying a
constant called common
ratio.
Example:
3,9,27
,81,24
3,…

25. Harmonic sequence is
a sequence such that
the reciprocals of the
terms form an
arithmetic sequence.
Example:
If we take the
reciprocals of
the terms of the
harmonic
sequence
½,1/4,1/6,/1/8…
then the
sequence
becomes 2, 4, 6,
8, ... which is an
arithmetic
sequence.

26. A Fibonacci sequence is a
sequence where its first two
terms are either both 1, or 0 and
1; and each term, thereafter, is
obtained by adding the two
preceding terms.
Example:
0, 1, 1,
2, 3,
5, …