DAY 92 – GEOMETRIC SEQUENCES

(DAY2)

VOCABULARY

Two types of sequences were studied:

Arithmetic Sequence: A sequence is called arithmetic if there is a real number d such that each term in the sequence is the sum of the previous term and d.

Geometric Sequence: A sequence is called geometric if there is a real number r such that each term in the sequence is a product of the previous term and r.

List the first five terms of each sequence, and identify them as arithmetic or geometric.

1.

2.

21141 )= and A( for n)=A(n)+A(n+

8114

11 )= and A(*A(n)for n)=A(n+

List the first five terms of each sequence, and identify them as arithmetic or geometric.

1.

-2,2,6,10,14 Arithmetic

2.

Geometric

21141 )= and A( for n)=A(n)+A(n+

8114

11 )= and A(*A(n)for n)=A(n+

32

1 ,

8

1 ,

2

1 ,2 ,8

3.

4.

611191 )= and A( for n)=A(n)A(n+

6113

21 )= and A( A(n)for n)=A(n+

3.

–6, – 25, – 44, – 63, – 82 Arithmetic

4.

Geometric

611191 )= and A( for n)=A(n)A(n+

6113

21 )= and A( A(n)for n)=A(n+

27

32,

9

16,

3

8,4,6

NTH TERM OF AN GEOMETRIC SEQUENCE

Every geometric sequence can be defined using the

explicit formula:

Where:

an nth term

a1 1st term

n term number

r common ratio

1 31

1 nraa n

n

WORD PROBLEM 1

A rabbit population grew in the following pattern: 2, 4, 8, 16, . . . If all the rabbits live and the pattern continues, how many rabbits will be in the 8th generation?

SOLUTION

rabbits 256

)2(*2

8

doubling - 2

2

18

8

1

1

1

a

n

r

a

raa n

n

PROBLEM

Consider the equation y = 150(2x )

a. Make a table x and y – values for whole-number x-values from 0 to 5.

b. What do the numbers 150 and 2 in the equation tell you about the relationship?

x 0 1 2 3 4 5

y

ANSWER KEY

Consider the equation y = 150(2x )

a. Make a table x and y – values for whole-number x-values from 0 to 5.

b. What do the numbers 150 and 2 in the equation tell you about the relationship?

150 is the initial value

2 is the growth rate

x 0 1 2 3 4 5

y 150 300 600 1200 2400 4800

WORD PROBLEM 2

Fido did not have fleas when his owners took him to the kennel. The number of fleas on Fido after he returned from the kennel grew according to the equation f = 8(3n). Where f is the number of fleas returned from the kennel. (Fido left the kennel at week 0.)

a. How many fleas did Fido pick up at the kennel?

b. What is the growth factor for the number of fleas?

c. How many fleas will Fido have after 10 weeks if he is not treated?

ANSWER KEY

Fido did not have fleas when his owners took him to the kennel. The number of fleas on Fido after he returned from the kennel grew according to the equation f = 8(3n). Where f is the number of fleas returned from the kennel. (Fido left the kennel at week 0.)

a. How many fleas did Fido pick up at the kennel?

8

b. What is the growth factor for the number of fleas?

3

c. How many fleas will Fido have after 10 weeks if he is not treated? 8(310) = 472,392