3. Stillrememberthis?
3
The sitting arrangement done last year when you
took the NCAE. There were 30 students in each
room. The table 1 shows that the number of
students varies directly as the number of rooms or
as the number of rooms increases, the number of
students also increases. Can you guess the number
of students when there are 12 rooms used? Table 1
is an example of Arithmetic Sequence.
4.
5. 5
Suppose that the number of a certain bacteria
grows as shown in table 2 below. At the start, there
are only 1, 000 bacteria and after 1 hour the
number of bacteria is doubled. It is consistent that
based from the observation, the number of bacteria
is always doubled every hour. Can you tell the
number of bacteria after 7 hours? 10 hours? Table
2 is an example of Geometric Sequence
6. 6
1. What have you
observed about the
differences of the
arithmetic and
geometric sequence?
7. 7
2. Can you tell the
number of students who
took the NCAE if there
were 12 rooms used
during the
examination?
8. 8
3. How many bacteria
would there be after 7
hours if we consider the
data in table 2?
9. 9
4. Can you define
arithmetic sequence?
Geometric sequence?
24. 24
Example 1. Examine the sequence
12, 17, 22, 27, 32, …
Step 1. Subtract the second term by the first term
𝑑 = 17 – 12 = 5 (d = right term – left term)
Step 2. Check if the difference between the third
term and the second term is the same with step 1.
𝑑 = 22 – 17 = 5 (d = right term – left term)
Step 3. Therefore, the sequence
12, 17, 22, 27, 32, … has a common difference,
25. 25
Example 2. Examine the sequence 2, 6, 18, 54, 162 …
Step 1. Divide the second term by the first term
𝑟 =
6
2
= 3 (r = right term divided by the left
term)
Step 2. Check the result if the same operation is applicable
to get the third term.
𝑟 =
18
6
= 3 (r = right term divided by the left
term)
Step 3. Therefore, the sequence 2, 6, 18, 54, 162 …has a
common ratio, r
27. 27
Arithmetic Sequence is a sequence where each term after the
first is obtained by adding the same constant, called the
common difference.
Common Difference is a constant added to each term of an
arithmetic sequence to obtain the next term of the sequence.
Geometric Sequence is a sequence where each term after the
first is obtained by multiplying the preceding term by a
nonzero constant called the common ratio.
Common Ratio is a constant multiplied to each term of a
geometric sequence to obtain the next term of the sequence.
29. 29
2. What is common difference?
Common ratio? State whether the
given sequence is an arithmetic or
geometric ?
a. 77, 70, 63, 56, 49 …
b. 6400, −1600, 400, −100, 25 …
c. 6, 30, 150, 750, 3750 …
