Assignment, pencil, red pen,
highlighter, textbook, GP notebook,
calculator
Suppose you have the sequence 2, 6, …, but you are not sure if it
is arithmetic or geometric. Since you do not know for sure,
a) determine the next 3 values
b) write the rule for each sequence.
c) determine whether or not 1002 is a term in either sequence.
ARITHMETIC
2, 6, ___, ___, ___
GEOMETRIC
2, 6, ___, ___, ___
total:
14
Suppose you have the sequence 2, 6, …, but you are not sure if it is
arithmetic or geometric. Since you do not know for sure,
a) determine the next 3 values
total:
b) write the rule for each sequence.
14
c) determine whether or not 1002 is a term in either sequence.
ARITHMETIC
GEOMETRIC +1
10 ___,
18 54
18 +1
14 ___
2, 6, ___,
2, 6, ___,
___, 162
___ , 486 , 1458
t(n) = 4n + 2
+2
1002 = 4n + 2 +1
1000 = 4n
250 = n +1
Yes, 1002 is a term in the
sequence since n is a positive,
whole number.
+2
t(n) = 2 (3)n +2
No, 1002 is
+1 not part of the
sequence. +2
1002 = 2(3)n
2
2
501 = (3)n +1
We cannot solve this equation… yet.
In the meantime, expand the
sequence to see if 1002 is part of it.
BB – 73
Consider the sequence 3, 6, 12, 24, …
a) What kind of sequence is it? How is it generated?
The sequence is geometric since the generator is “multiply by 2.”
b) Pairing the values in the sequence with their position in the
sequence creates the table below. Copy the table and continue it to
include the next five terms of the sequence.
n
t(n)
0
3
1
6
2
12
3
24
4
5
6
7
8
48
96
192
384
768
c) How many times do we multiply the initial value of 3 by 2 in order to
obtain the value of 24 in the sequence?
24 = 3  2  2  2
We multiply by 2 three times.
d) Is there a short cut for doing repeated multiplication? What is it?
Yes, the shortcut is using exponents.
BB – 73
n
t(n)
Consider the sequence 3, 6, 12, 24, …
0
3
1
6
2
12
3
24
4
5
6
7
8
48
96
192
384
768
e) The value found when n = 6 can be obtained by multiplying
3  2  2  2  2  2  2. Rewrite this expression using exponents.
3 (2)6
f) What will the representation be for the hundredth term of the
sequence?
3 (2)100
g) How could you represent t(n)?
t(n) = 3 (2)n
BB – 74
A tank contains 8000 liters of water. Each day, one–half of
the water in the tank is removed.
Make a table and fill in the first 5 terms and identify whether this is an
arithmetic or geometric sequence. What is the generator?
n
0
1
t(n)
8000
4000
2
3
2000 1000
This is a geometric sequence.
4
5
500
250
The generator is multiply by ½.
How much water will be in the tank after:
a) the
6th
b) the
12th
c) the
nth
day?










6
t (6)  8000 1  125 liters remain by the 6th day.
2
12

day? t (12)  8000 1   1.95 liters remain by the 12th day.
2 
day?










t (n)  8000 1
2





n
Multiplier The number by which you multiply in order to increase (or
decrease) something by a given percentage in one step.
The ECHS cafeteria increased the cost of its $2.25
sandwiches by 60%. What is the new price?
100%
What percentage represents the original, “whole” cost? _______
Add the percent increase of 60% to the “whole”:
100%
+ 60%
160%
1.60
Change the percent to a decimal. This is the MULTIPLIER: _______
$2.25 (1.60) = $3.60
Determine the new cost. ___________________
The sandwiches
now cost $3.60.
Determine the multiplier for each example.
a) 20% mark–up on books
100%
+ 20%
120%
1.20
c) 47% increase in profit
100%
+ 47%
147%
1.47
e) 15% decrease in productivity
100%
– 15%
0.85
85%
b) 13.5% increase in bacteria
population
100.0%
+ 13.5%
1.135
113.5%
d) 8.25% sales tax in Los Angeles
100.00%
+ 8.25%
108.25%
1.0825
f) 30% off sale at Sears
100%
– 30%
0.70
70%
BB – 75
Newspaper Headline:
FLU EPIDEMIC HITS TEXAS TOWN!
30% increase in cases reported this week!
Today there were 100 cases reported to begin the annual flu season.
Make a table for this sequence.
n
t(n)
0
1
2
3
4
100
130
169
220
286
…
n
a) Represent the current percentage of cases in decimal
form. 100%  1.00 (We always start with 100%.)
b) Change the 30% increase to a decimal. 30%  0.30
c) To increase something by 30%, we will use the
MULTIPLIER: 1.00 + 0.30 = 1.30
d) Fill in the table and find a rule for the number of
cases for the nth week.
100(1.3)n
t(n) = 100(1.3)n