### Geometric/Exponential

```Geometric/Exponential
Sequences
t n  ar  , n  1, n  N
n
Mathematics 3204/05
1.
(B)
(C)
(D)
5.
 12 , 13 , 92 , 274 , 818 ,  ?
arithmetic
cubic
exponential
logarithmic
Which pattern below represents a geometric sequence?
(A)
4.
{1, 2,3,5,8, }
{1, 2, 4,8,16, }
{1, 4, 7,10,13, }
{1, 4,9,16, 25, }
What type of sequence is
(A)
(B)
(C)
(D)
3.
Exponential Sequences
Which sequence represents an exponential function?
(A)
(B)
(C)
(D)
2.
Public Exam Questions
2  3, 2  3  3, 2  3  3  3, 
2  4, 2  5, 2  6, 
2  3, 2  3 , 2  3 , 
2  3, 2  3 , 2  3 , 
2
2
3
3
Which type of sequence is depicted by the phone tree shown?
(A)
cubic
(B)
geometric
(C)
(D)
quartic
Which situation would be best modeled by an exponential relationship?
(A)
(B)
(C)
(D)
depth of water in a cylindrical tank as it is filled with 30L of water each
minute
height of a rock thrown in the air from the time it is thrown until it hits the
ground
height of the sun above the horizon over a 24 hour period
value of a lawnmower that depreciates by 15% annually
115
2007-2008
Mathematics 3204/05
6.
(A)
tn  2n  3
(B)
tn  n 2  3
(C)
tn  2n
n
tn 
3
You put one penny in a glass jar one day, three pennies the next day, and so on,
tripling the number of pennies put in the jar each day thereafter. What type of
sequence will this pattern create?
(A)
(B)
(C)
(D)
8.
cubic
geometric
quartic
Which pattern represents a geometric sequence?
(A)
(B)
(C)
(D)
9.
Exponential Sequences
Which function represents a geometric sequence?
(D)
7.
Public Exam Questions
13  2, 13  2  2, 13  2  2  2, 
13  2, 13  3, 13  4, 
13  2, 13  2  2, 13  2  2  2, 

1
3

 21 , 13  22 , 13  23 ,
Which represents an exponential relationship?
(A)
x 1 1.2 1.4 1.6 1.8
y 3
(B)
x
1
y 5.5
(C)
x
1
y 5.5
(D)
6
8
12
15
1.8 2.6 3.4
7
9.5 13 17.5
1.5
9
4.2
2
2.5
18.5 37
x 1 1.1 1.2
1.3
3
67.5
1.4
y 6 36 216 1296 7776
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2007-2008
Mathematics 3204/05
10.
Exponential Sequences
Which represents a geometric sequence?
(A)
(B)
(C)
(D)
11.
Public Exam Questions

1
2
 3, 12  3  3, 12  3  3  3, ...


2

3 , ... 
3
1
2
3,
1
2
 3 , 12  3 , ...
1
2
3,
1
2
 3 , 12 
 12  2,
1
2

2
3
 3, 12  4, ... 
Which represents an exponential relationship?
(A)
x 1 2 3 4 5
y 6 3
(B)
3
2
x 1 2 3
3
4
3
8
4
5
y 6 3 0 3 6
(C)
x 1 2
3
4
5
y 6 8 11 15 20
(D)
x 1 2
3
4
5
y 6 8 10 12 14
12.
Which represents a geometric sequence?
(A)
(B)
(C)
(D)
 12  1 2, 12  2  2, 12  3  2, 12  4  2, ... 
 12 1 2, 12  2  2, 12  3  2, 12  4  2, ... 


1
2
1
2
 21 ,
1
2
 22 ,
1
2
 23 , 12  24 , ... 
 21 , 12  22 , 12  23 , 12  24 , ... 
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Mathematics 3204/05
13.
Public Exam Questions
Exponential Sequences
Which pattern represents an exponential sequence?
(A)
Figure 1 Figure 2
Figure 3
(B)
Figure 4
Level 1
Level 2
Level 3
Level 4
(C)
Figure 1
Figure 2
Figure 3
Figure 4
(D)
Figure 1
Figure 2
Figure 3
Figure 4
14.
Which represents an exponential relationship?
(A)
(B)
(C)
(D)
x 1 2 3 4
y 1
1
2
1
3
1
4
x 1 2
3
4
1
3
1
27
1
81
y
1
9
x 1 2 3 4
y 3 5 7 9
x 1
2
3
4
y 2 4 4 2
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2007-2008
Mathematics 3204/05
15.
Public Exam Questions
Exponential Sequences
Which
best represents an exponential relationship?
5– 5
10
15
20
2– 4
4
6
8
2
y
(A)
20
15
(4, 13)
10
(2, 7)
(1, 4)
(0, 1)
2
4
5
– 4 – 2
20
5
10
15
– 5
2– 4
4
6
8
2
6
8
x
6
8
x
8
x
8
x
– 5
y
(B)
20
(3, 16)
15
10
(2, 9)
5
(1, 4)
20
5
10
15
– 5
2– 4
4
6
8
2
(0, 1)
2
– 4 – 2
4
– 5
y
(C)
20
(4, 16)
15
10
(3, 8)
5
20
5
10
15
– 5
2– 4
4
6
8
2
(0, 1)
– 4 – 2
(2, 4)
(1, 2)
2
4
6
– 5
y
20
(D)
(3, 28)
15
10
(2, 9)
5
(0, 1)
– 4 – 2
(1, 2)
2
4
6
– 5
16.
Which represents an exponential sequence?
(A)
(B)
(C)
(D)
2, 2  3, 2  6, 2  9, 2 12,...
2, 2  3, 2  6, 2  9, 2 12,...
2, 2  3, 2  3 , 2  3 , 2  3 ,...
2, 2  3, 2  3 , 2  3 , 2  3 ,...
2
3
2
4
3
4
119
2007-2008
Mathematics 3204/05
15.
Public Exam Questions
Exponential Sequences
What type of function is illustrated by the graph shown?
y
(3,27)
(2,16)
(A)
(B)
(C)
(D)
16.
cubic
exponential
linear
(1,7)
(0,0)
x
Which represents a geometric sequence?
(A)
(B)
(C)
(D)
1 5 7 
 ,1, , ,...
3 3 3 
 16 32 64 
8, , , ,...
 3 9 27 
 2 8 32 
 , , 6, ,...
3
3 3

128 
 2 16
,...
 , ,18,
3
3 3

120
2007-2008
Mathematics 3204/05
Public Exam Questions
Exponential Sequences
1. B
2. C
3. C
4. B
5. D
6. C
7. B
8. C
9. D
10. A
11. A
12. D
13. B
14. B
15. C
16. C
15. D
16. B