This slide focuses on the definition of an arithmetic sequence and finding the common difference.

1. ARITHMETIC
SEQUENCE
Solomon Hippocrates S. Flores
E. Rodriguez Vocational High School

2. How many wheels do you see?

3. How about on this one?

4. And on this?

5. What if 10 tricycles pass by, how
many wheels would you see? How
about 15 tricycles?

6. The above situation will give us the following list:
3, 6, 9, … a10
and
3, 6, 9, … a15.
Can we find a way to
actually determine the
number of wheels of n
number of tricycles
without actually
seeing or counting
one?

7. Consider the following
sequences:
1) 4, 5, 6, 7, …
2) - 4, - 7, - 10, - 13, …
3) 1.5, 2.5, 3.5, 4.5, …
Find out how the succession
of terms is obtained.

8. The sequences above show that a
constant, either positive or
negative, is added to the preceding
term to get the next term.
Such situation is
called an
Arithmetic
Sequence.

9. An arithmetic sequence is a
sequence in which any term is
obtained by adding a constant to the
preceding term. The number added to
any term to get the next term is the
difference between two successive
terms, hence, the common difference,
denoted by d, which can either be
positive or negative.

10. Determine if the following sequence is
arithmetic or not. If yes, find the common
difference d and identify the next term.
1) 5, 12, 19, 26, …

11. 2) 0.6, 3.1, 5.6, 8.1, …

12. 3) 5, 2, -1, -4, …

14. 5) 2, 3, 5, 7, …

16. 7) 3, 8, 13, 18, …

17. 8) -11, -5, 1, 7, …

18. 9) -12, -8, -5, -1, …

19. 10) -3, -1, 1, 3, …

21. 12) 11, 8, 5, 2, …

22. 13) 5, 10, 15, 20, …

23. 14) 0, -3, -6, -9, …

24. 15) -80, -1, -78, …

25. VALUES INTEGRATIONDiligence can
help bring
you to a
targeted
end.Name a sequence
of steps that you
can set for yourself
when aiming for a
target.

26. Complete the
following
statements:
1. An arithmetic sequence is a
sequence in which any term is
obtained by ______ a _________ to
the ______________ terms.
2. The common difference, d, is the
_______ added to _____ term to get the
_____ term which can either be
__________ or __________.

27. Find the common difference, d, in
each of thefollowing sequence.
,
,
1) -2, 4, 10, … 6) 28.5, 26.3, 24.1, …
2) -21, -15, -9, … 7) 5, -1, -7, …
3) -18, -16, -14, … 8) -16, -12, -8, …
4) 1.5, 3, 4.5, … 9) , , , …
5) 4x, -3x, -10x, … 10) 4.5, 2.1, -0.3, …

28. Assignment
Determine if the following sequence is arithmetic
or not. If yes, find the common difference and identify
the next term.
1) -2, 4, 10, …
2) 2, -2, 2, -2, …
3) 4.5, 2.1, -0.3, …
4) 6, 12, 19, 26, …
5) 5, -1, -7, …

29. Thank you!