Grade 10 Mathematics

1. TOPIC: Searching
for Patterns in
Sequences
Subtopic:
Geometric
Sequence

2. DRILL/ REVIEW
Direction: Find the ratio of the second number to the
first number.
1. 2 and 8
2. -3 and 9
3. 1 and ½
4. -5 and -10
5. 12 and 4
6. -49 and 7
7. ¼ and ½
8. a2 and a3
9. k – 1 and k
10. 3m and 3mr
4
-3
1/2
2
1/3
-1/7
2
a
k/k-1
r

3. REVIEW
 Snowball

(mastery)
Students will have
fun locating the
answers to questions
after tossing
wads of paper across
the room.

4.  Direction: Determine if the following sequence is
arithmetic or not.
 1.3, 12, 21, 30, …
 2.8, 3, -2, -7, …
 3.5, 12, 19, 26, 33, …
 4.-1, 7, 15, 23, …
 5.32, 16, 8, 4, 2, …
 Guide Questions:
 6.How do you describe the pattern in no. 5?
 7.Can you call that an arithmetic sequence? Why?
 8.What do you observe about their ratio?Let’s get the ratio
of two consecutive terms (right to left)
 32, 16, 8, 4, 2, … 2/4 = 4/8 = 8/16 = 16/32 .
The ratio is ½.
ARITHMETIC
ARITHMETIC
ARITHMETIC
ARITHMETIC
NOT

5. LESSON PROPER
 GEOMETRIC
SEQUENCE is a
sequence where each
term after the first term
is obtained by
multiplying the
preceding term by a
nonzero constant
called COMMON
RATIO (r).

6.  Direction: State whether
each of the following
sequence is geometric or
not.
 1. 5, 20, 80, 320, …
 2. 7√2 , 5√2 , 3√2 , √2
 3. 5, -10, 20, -40, …
 4. 1, 0.6, 0.36, 0.216, …
 5. 10/3, 10/6, 10/9, 10/15, …
Geometric
not
Geometric
Geometric
Not
SOLUTION:
1. r = 320/80 = 80/40 = 20/5 = 4 2. r = √ 2 / 3 √2 = 0.97
r = 3√2 / 5√2 = 0.6
NOT
3. r -40/20 = 20/-10 = -10/5 = -2
4. r = 0.216/0.36 = 0.36/0.6 =0.6/1 = 3/5 or 0.6

7. PRACTICE EXERCISE
 Tell whether or not each of the following
number is a geometric sequence.For those that
are geometric, give the common ratio.
 1. 8 , 8 , 8 , 8 ,....
 2. 1, 4, 9 ,16 ,25 ,......
 3. 1 , 4 , 16 , 256 , .....
 4. 1 , 3 , 9 , 27 ,......
 5. 5 , 15 , 25 , 35 , .....
Yes r = 1
NO
YES r = 4
YES r = 3
NO

8. GENERALIZATION
How do you
differentiate
arithmetic to
geometric
sequence?
 Arithmetic sequence is a
sequence where each term
after the first is _______ a
fixed number called _____
 _________, while
geometric sequence is a
sequence where each term
after the first is _________
 by a non zero constant
called
_________________
added
common
difference
multiplied
common ratio.

9. ASSIGNMENT
Create their
own pattern
that describes
geometric
sequence.