CHAPTER 9 TEST A
Directions: Show all work.
Name: ______________________
Section: _____________________
 3 4 5
1. Which one of the following formula will produce the sequence  2, , , ,
 2 3 4
n 1
a. an 
n2
2
n
b. an  2
n 1
n 1
d. an 
n
2n
c. an 
2n  1
e. an

?

 1

n
2n
n 1
2. The Pell sequence is defined recursively by
P0  0, P1  1, Pn 2  Pn  2 Pn 1
Which one of the following gives the first 6 terms of the Pell sequence?
a. 0,1, 2,5,12, 29
b. 0,1,1,3,5,11, 21
c. 0,1, 2,3,5,8
d.
0, 2, 4,10, 24,58
e.
0, 2, 2,6,10, 22
0, 2, 2, 4,6,10
f.
3. Which one of the following gives the first 5 terms of the geometric series with
a  10 and r  1.1 ?
a. 10,11.1,12.2,13.3,14.4
b. 10,11,12.1,13.31,14.641 c. 10,11,12,13,14
d. 10,11,12.1,13.21,14.321 e.
10,10.1,10.2,10.3,10.4
f.
10, 21,32, 43,54
4. Which one of the following is a simplification of the sum
M   M  r    M  2r    M  3r     M  11r  ?
a. M  55r
b. 11M  66r
c. 11M  55r
d. 12M  66r
e. 12M  55r
5. Which one of the following series is geometric?
10
a.
 2k
k 1
10
10
b.
 i2
i 1
c.
10
10
2 j
d.
j 1
1

n 1 2 n
e.
m
1/ 2
m 1
6. Which one he following is equivalent to 12  x  ?
3
a. 36  3x
d. 1728  x 3
b. 1728  144 x  12 x 2  x3
e. 1728  288 x  24 x 2  x3
c. 36  24 x  12 x 2  x3
f. 1728  432 x  36 x 2  x3
7. Find the next three terms of the arithmetic sequence: 7, 24, 41,
Chapter 9/Form A
.
 43 60
8. Find the 14th term in the arithmetic sequence: 2, , ,
 13 13



n 1
 1  n  1

9. Find the first four terms in the sequence whose nth term is cn
n2  1
2
.
10. Find the first five terms of the sequence of the recursively defined sequence:
1
A1  100,
An 1  An  10
2
11. A filter is designed to remove 12% of a contaminant from a fluid per pass. If there
are initially 75 grams of contaminant in the fluid, find a formula for the amount of
contaminant in the fluid after n passes through the filter.
 2 
12. Find the sum of the first 15 terms of the sequence: an   5  n  .
 3 

13. Find the sum of the first 5 terms of the sequence: an   2  3
.
n 1
14. An investor deposits $12 into a stock on the first month, $24 more on the second
month, $36 on the third month and, in general, $12n on the nth month. How much
will the investor have deposited in the stocks after 30 months?
4
15. Write the series

k 1
 1
k 1
2k 2
in expanded form. Simplify each term in the expansion.

16. Evaluate the infinite series:
23
 3  5 
k 1
k 1
.
17. Find a fraction equivalent to the decimal: 0.17 .
5
1

18. Write  x   in descending powers of x.
x

19. What is the coefficient of x3 y14 in the expansion of  x  y  ?
17
20. Annie borrowed $60,000 at 8% annual interest for a small business venture. If she
pays $500 per month towards the loan, how much does she owe after n months?
Chapter 9/Form A
Hint: Work out the first few months to find a formula for the nth month.
n
 2 
21. Use a calculator to approximate  
 .
n1  1  5 
20
22. Approximate to five significant digits the 50th term in the sequence

an   1.0002 
12n
.
23. Use a calculator to evaluate many terms for the recursive sequence defined by:
1
a1  17,
an1 
an  1
What happens to the sequence as n increases?
100
24. Use a calculator to approximate
 50 1.0775
n 0
n
to the nearest thousandth.
25. Use a calculator to find the number of ways of choosing a collection of ten marbles
from a collection of 17 marbles: 17 C10 .
Chapter 9/Form A
Solutions For Chapter 9 Test Form A.
1. d
2. a
7. 7, 24, 41, 58,75,92
3. b
4. d
5. a
6. f
17
 n  1  a14  2  17  19 .
13
9 8 25 

9. 2,  , ,  
5 5 17 

10. 100,60, 40,30, 25
8. an  2 
11. A1  75  0.12  75  0.88  75  A2   0.88 75  An   0.88 75 .
n
2
2
2 15
2 15 16 
5

n

15
5

n  75 
 155 .




3
3 n1
3 2
n 1
4
35  1 5
n
13.  2  3  2
 3  1  242 .
3 1
n 0
30
 30  31 
14. 12 n  12 
  $5580 .
n 1
 2 
15
12.
4
15.

k 1
 1
2k
k 1
2

1 1 1 1
   .
2 8 18 32
k 1
2 1
25 5
   .
3
3 1
32 3
5


k 1

17  1  17
 1 
17. 0.17  0.17 

 .
 
100  1  1  99
k 1  100 


 100 
16.
23

 
k 1 3  5 


5
2
3
4
1

1
1
1
1 1
18.  x    x5  5 x 4    10 x3    10 x 2    5 x     
x

x
 x
 x
 x  x
10 5 1
 x5  5 x3  10 x   3  5 .
x x x
17  17! 17 16 15 

 17  8  5   680 .
19.   
3 2
 3  3!14!
Chapter 9/Form A
5
20. A1  60000 1.006   500 ,


A2  60000 1.006   500 1.006  500  60000 1.08   500 1.006   500
2
A3  60000 1.006   500 1.006   500 1.006   500
3
2
n 1
An  60000 1.006   5001.006 k  60000 1.006   500
n
k 1
 75000  15000 1.006 
n
1.006 n  1
0.006
n
21. On the TI-85, the sum can be found
using the SUM SEQ on the MATH
menu, as shown to the right:
22. a50  1.0002
600
 1.12748 .
23. Get the sequence started and then keep hitting “Enter” to produce values as shown.
The sequence approaches 0.61803
100
24.
 50 1.0775  50
n
n 0
25.
17
C10 
1.0775101  1
 1212222.632 .
0.0775
17!
 19448
10! 7!
Chapter 9/Form A