G R O U PT H R E E

W A T C H &L E A R N

I NI T I A L I ZI NG. . .

A sequence is an ordered list of

numbers.

A sequence is a function whose domain is either

finite {1,2,3,…n} or infinite {1,2,3,…} set.

W E P R O U D L YP R E S E N T T O

Y O U :

O M E T R IS E Q U E N C E S

A N DE O M E T R I

M E A N

EG C

CG

Geometric Sequence

Geometric Mean

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

Geometric Sequence

Take a look…-1, -2, -4, -8, -16, -32,…

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.

Tools and Techniques for Quality Improvement

-1, -2, -4, -8, -16, -32,…

a1

-1a2 = a1r

-2 = -1(2)

a3 = a2r = (a1r)r = a1r2

-4=-2(2)= -1 (2)(2)= -1(2)

a4 = a3r = a1(r)r(r) = a1r3

-8=-4(2) =-1(2) (2)(2)= -1(2)

Geometric Sequence

General Rule

an=a1.rn-

1

1st term of the sequence

Common ratio

Number of terms

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 = 2n=5a5=?

Solution:an= a1

.rn-1

a5 = ₱ 100 (2)5-1 a5 = ₱ 100 (2)4 a5 = ₱ 100 (16)a5 = ₱ 1600

Answer:₱1600

Geometric Sequence

EXAMPLES

1 2 3 4

Given that a1 = -3.5, r = 4 and an = -224, find the

value of n.

Given:a1=-3.5r = 4

an=-224n=?

Solution:an= a1

.rn-1

-224=-3.5(4n-1)64=4n-1

22n-2=26

2n-2=62n=6+2n=4

Answer:4

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.

The first and the last terms of a geometric sequence are called Extremes

The terms between them are called Means

5, 25, 125, 625

Formula:To solve for a Geometric

Mean between two terms.

Find the geometric mean between 3 and 48.

3(48)

3(48)

144

Answer: 12

If there are more, use the general term for geometric

sequence.

an=a1.rn-1

Geometric Mean

EXAMPLES

1 2 3 4

Insert 3 geometric means

Between 4 and 1024.

Given:a1=4

a5=1024r=?

a2, a3, a4=?

Solution:a5=a1rn-1

1024=4r4

√256=√r4

r=4

a2=4(4) 1=16a3=4(4) 2=64a4=4(4) 3=256=16, 64, 256

Answer:4, 16, 64, 256, 1024

Ratio Formula

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 = 3a2 = 6a3 = 18

Your turn!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.

THANK YOU!!!

Submitted by:

Richelle Mae E. PadillaAngel Mae B. RuizReenie Trisha VergaraShemm L. MadridMarx Chryx Del Mundo