The document explains sequences in mathematics, focusing on arithmetic sequences where terms follow a specific pattern with a constant difference. Examples illustrate both finite and infinite sequences, as well as the formulas used to compute terms and common differences or ratios. It includes practical examples such as Marvin's guitar practice schedule and a seating arrangement scenario for a concert.

1. sequen
ces
and
ARITHMETIC SEQUENCES

2. -in mathematics, it is a string of
objects, like numbers, that follow a
particular pattern. The individual
elements in a sequence are called
terms.
SEQUE
NCE

3. - is a list of things (usually numbers)
that are in order.
-some of the simplest sequences can
be found in multiplication tables:
SEQUE
NCE

4. exampl
es
3, 6, 9, 12, 15, 18, 21, …
Pattern: “add 3 to the previous number to get the next
number”
0, 12, 24, 36, 48, 60, 72, …
Pattern: “add 12 to the previous number to get the next
number”

5. exampl
es
10,–2 8,×2 16,–2 14,×2 28,–2 26,×2 52, …
Pattern: “alternatingly subtract 2 and multiply by 2 to get
the next number”
0,+2 2,+4 6,+6 12,+8 20,+10 30,+12 42, …
Pattern: “add increasing even numbers to get the next
number”

6. SEQUENCE
When the sequence goes on forever it is called an infinite
sequence,
otherwise it is a finite sequence

7. exampl
es
{1, 2, 3, 4, ...} is a very simple sequence (and it is
an infinite sequence)
{20, 25, 30, 35, ...} is also an infinite sequence
{1, 3, 5, 7} is the sequence of the first 4 odd numbers (and
is a finite sequence)

8. exampl
es
{1, 2, 4, 8, 16, 32, ...} is an infinite sequence where every
term doubles
{a, b, c, d, e} is the sequence of the first 5
letters alphabetically

9. arithmeti
cSEQUENCE
In an arithmetic sequence, the difference between
consecutive terms is constant. The constant difference is
denoted by d.

10. arithmeti
cSEQUENCE
FORMULA: an= a1 + (n-1) d

11. exampl
es

12. exampl
es

13. exampl
es

14. exampl
es
Find the common difference and the next term of
the following sequence:
3, 11, 19, 27, 35,...

15. exampl
es
To find the common difference, you have to subtract a pair of terms. It
doesn't matter which pair you pick, as long as they are right next to
each other:
11 – 3 = 8
19 – 11 = 8
27 – 19 = 8
35 – 27 = 8
The difference is always 8, so d = 8. Then the next term is 35 + 8 = 43.

16. exampl
esFind the common ratio and the seventh term of
the following sequence:
2/9, 2/3, 2, 6, 18,...

17. exampl
esTo find the common ratio, you have to divide a pair of terms. It
doesn't matter which pair you pick, as long as they're right next to
each other:
The ratio is always 3, so r = 3. Then the sixth term is (18)(3) = 54 and
the seventh term is(54)(3) = 162.

18. exampl
esMarvin is practicing the guitar for a competition. He starts
by practicing the guitar for 30 minutes on the first day and
then increases the practice time by 10 minutes each day. If
the pattern continues, how many minutes will he spend
practicing on the 7th day?

19. exampl
esa1 = 30 minutes
d= 10 minutes
a7 = ?

20. exampl
esFORMULA: a7= 30 + (7-1) 10
= 30 + 60
= 90 minutes

21. exampl
esEd Sheeran’s concert venue has 100 rows of seats
with 30 seats in the first row, 35 seats in the second
row, 40 seats in the third row and so on. How many
seats are there in the 69th row?

22. exampl
esa1 = 30 seats
d= 5 seats
a69 = ?

23. exampl
esFORMULA: a69= 30 + (69-1) 5
= 30 + 340
= 370 seats

24. Prepared by:- Daphne Millen Arenas
-Kent Daryl Acuna
-Marvin Dale Lopez
- Angelicka Kim Batalla
- Ericka Lei Gamalong