Group Members: Shemm Madrid Marx Del Mundo Angel Mae Ruiz Reenie Trisha Vergara Richelle Mae Padilla

1. G R O U P
T H R E E
W A T C H &
L E A R N

2. I N I T I A L I Z I N G . . .

3. A sequence is an
ordered list of
numbers.

4. W E P R O U D L Y
P R E S E N T T O
Y O U :
O M E T R I
S E Q U E N C E S
A N D
E O M E T R I
M E A N
EG C
CG

5. Geometric Sequence
Geometric Mean

6. When each term in a sequence is
found by multiplying the previous
term by a constant, it is called
Geometric Sequence

7. Each term is multiplied by 2 to get the
preceding terms.
The 1st term (a1)is -1.
To obtain the second term, the common
ratio (r) is multiplied to a1.

8. Tools and Techniques for Quality
Improvement
a1
a2 = a1r
a3 = a2r = (a1r)r = a1r2
a4 = a3r = a1(r)r(r) = a1r3

9. Geometric Sequence
General Rule
1st term of the sequence
Common ratio
Number of terms
an=a1
.rn-1

10. Geometric Sequence
EXAMPLES
1 2 3 4
Mr. Rivera wants to save money on his
bank account. He decided to double the
amount of money that he will deposit every
month. He started to save ₱ 100 on his
bank account. About how much will he save
after 5 months?
Given:
a1=₱ 100
r = 2
n=5
a5=?
Solution:
an= a1
.rn-1
a5 = ₱ 100 (2)5-1
a5 = ₱ 100 (2)4
a5 = ₱ 100 (16)
a5 = ₱ 1600
Answer:
₱1600

11. Geometric Sequence
EXAMPLES
1 2 3 4
Given that a1 = -3.5, r = 4
and an = -224, find the
value of n.
Given:
a1=-3.5
r = 4
an=-224
n=?
Solution:
an= a1
.rn-1
-224=-3.5(4n-1)
64=4n-1
22n-2=26
2n-2=6
2n=6+2
n=4
Answer:
4

12. Geometric Mean
RatioFormula

13. Geometric Mean
EXAMPLES
1 2 3 4
Insert 3 geometric mean
Between 4 and 1024.
Given:
a1=4
a5=1024
r=?
a2, a3, a4=?
Solution:
a5=a1rn-1
1024=4r4
256=r4
r=4
a2=4(4) 1=16
a3=4(4) 2=64
a4=4(4) 3=256
=16, 64, 256
Answer:
4, 16, 64, 256, 1024