Members: Shemm Madrid Marx Chryz Del Mundo Reenie Trisha Vergara Angel Mae Ruiz 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. A sequence is a function
whose domain is either
finite {1,2,3,…n} or
infinite {1,2,3,…} set.

5. 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

6. Geometric Sequence
Geometric Mean

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

8. 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.

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

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

11. 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

12. 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

13. is a type of mean or average, which indicates
the central tendency or typical value of a set
of numbers using the product of their values.
Geometric Mean
That means you multiply a bunch of numbers
together, and then take the nth root, where n
is the number of values you just multiplied.

14. The first and the last terms of a geometric
sequence are called Extremes
The terms between them are called Means
5, 25, 125, 625

15. Formula:
To solve for a Geometric
Mean between two terms.

16. Find the geometric mean
between 3 and 48.
3(48)
3(48)
144
Answer: 12

17. If there are more, use the
general term for geometric
sequence.
an=a1
.rn-1

18. Geometric Mean
EXAMPLES
1 2 3 4
Insert 3 geometric means
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

19. Ratio Formula

20. Geometric Mean
EXAMPLES
1 2 3 4
Find r and the missing
terms in the Geometric
Sequence (2,_,_,54)
r=3
2, 2(3),2(3)(3), 54
2, 6, 18, 54
Answers:
r = 3
a2 = 6
a3 = 18

21. 1. Find the 9th term in the Geometric
Sequence 3, 9, 27, 81, 243.
2. Find the first term of a geometric
sequence whose fourth and seventh terms
are 108 and 2916.
3. Find two geometric means between 128
and 16.

22. Submitted by:
Richelle Mae E. Padilla
Angel Mae B. Ruiz
Reenie Trisha Vergara
Shemm L. Madrid
Marx Chryx Del Mundo