Name: 
 

Module 4 Test


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Write a recursive rule for the sequence.
mc001-1.jpg
a.
mc001-2.jpg
c.
mc001-4.jpg
b.
mc001-3.jpg
d.
mc001-5.jpg
 

 2. 
A customer has a $100 gift card to a local coffee shop. Suppose the customer, using the card, spends $5 per day at the shop. Which recursive rule represents the card’s remaining balance mc002-1.jpg, in dollars, after using the card for mc002-2.jpg days?
a.
mc002-4.jpg and mc002-5.jpg for mc002-6.jpg
b.
mc002-7.jpg and mc002-8.jpg for mc002-9.jpg
c.
mc002-10.jpg and mc002-11.jpg for mc002-12.jpg
d.
mc002-13.jpg and mc002-14.jpg for mc002-15.jpg
 

 3. 
A company is tracking the number of complaints received on its website. During the first 4 months, they record the following numbers of complaints: 20, 25, 30, and 35. Which is a possible explicit rule for the number of complaints they will receive in the nth month?
a.
mc003-1.jpg
b.
mc003-2.jpg
 

 4. 
Find the 16th term in the following arithmetic sequence.
–6, –13, –20, –27, –34, ...
a.
–105
c.
–126
b.
–118
d.
–111
 

 5. 
Find the first 5 terms of the sequence with mc005-1.jpg and mc005-2.jpg for mc005-3.jpg.
a.
1, 2, 3, 4, 5
c.
6, 12, 24, 48, 96
b.
6, 7, 8, 9, 10
d.
6, 11, 21, 41, 81
 

 6. 
Write a rule for the nth term of the arithmetic sequence. –10, –4, 2, 8, . . .
a.
mc006-1.jpg
c.
mc006-3.jpg
b.
mc006-2.jpg
d.
mc006-4.jpg
 

 7. 
Write a recursive rule for the sequence.
mc007-1.jpg
a.
mc007-2.jpg
c.
mc007-4.jpg
b.
mc007-3.jpg
d.
mc007-5.jpg
 

 8. 
Find a function that describes the arithmetic sequence 16, 17, 18, 19, ... Use y to identify each term in the sequence and n to identify each term’s position.
a.
y = 16n
c.
y = n + 15
b.
y = 15n +1
d.
y = 17n –1
 

 9. 
Julio is training for a swimming race. The first part of his training schedule is shown. Is this training schedule an arithmetic sequence? Explain. If Julio’s training schedule starts on a Tuesday and he swims every two days, on which day will he swim for 2.95 miles?
Session
1
2
3
4
5
6
Swimming distance (mi)
0.25
0.55
0.85
1.15
1.55
1.85
a.
Julio’s training schedule is an arithmetic sequence, because a constant increase of 0.3 occurs between the sessions. Julio will swim 2.95 miles on Thursday.
b.
Julio’s training schedule is not an arithmetic sequence, because the increase between session numbers and corresponding distances is not the same. Julio will swim 2.95 miles on Thursday.
c.
Julio’s training schedule is an arithmetic sequence, because a constant increase of 0.3 occurs between the sessions. Julio will swim 2.95 miles on Saturday.
d.
Julio’s training schedule is an arithmetic sequence, because a constant increase of 0.3 occurs between the sessions. Julio will swim 2.95 miles on Monday.
 

 10. 
Write a rule for the nth term of the sequence. Use your rule to find a100.
–8, 9, 26, 43, 60, . . .
a.
1692
c.
17
b.
1709
d.
1675
 

 11. 
What is the 20th term in the following geometric sequence?
–2, –6, –18, –54, –162, ...
a.
1,162,261,467
c.
2,324,522,934
b.
–6,973,568,802
d.
–2,324,522,934
 

 12. 
Find an explicit function rule for the sequence –3, 3, 9, 15, . . ..
a.
mc012-1.jpg
c.
mc012-3.jpg
b.
mc012-2.jpg
d.
mc012-4.jpg
 

 13. 
Find an explicit function rule for the sequence mc013-1.jpg .
a.
mc013-2.jpg
c.
mc013-4.jpg
b.
mc013-3.jpg
d.
mc013-5.jpg
 

 14. 
Write a rule for the nth term of the sequence. Use your rule to find a100.
–8, 0, 8, 16, 24, . . .
a.
8
c.
800
b.
784
d.
792
 

 15. 
Write a rule for the nth term of the sequence. Use your rule to find a30.
–4, 5, 14, 23, 32, . . .
a.
9
c.
257
b.
266
d.
275
 

 16. 
Write a rule for the nth term of the sequence. Use your rule to find a70.
–10, –8, –6, –4, –2, . . .
a.
130
c.
132
b.
2
d.
128
 

 17. 
A theater has 18 rows of seats. There are 22 seats in the first row, 26 seats in the second row, 30 seats in the third row, and so on. Which of the following is a recursive formula for the arithmetic sequence that represents this situation?
a.
mc017-6.jpg, mc017-7.jpg for mc017-8.jpg
b.
mc017-9.jpg, mc017-10.jpg for mc017-11.jpg
c.
mc017-12.jpg
d.
mc017-13.jpg
 

 18. 
Make a function table to represent the first five terms of the following sequence defined over the natural numbers: 20, 17, 14, 11, 8, . . ..
a.
mc018-1.jpg
b.
mc018-2.jpg
c.
mc018-3.jpg
d.
mc018-4.jpg
 

 19. 
Find the first five terms of the sequence defined over the natural numbers with the explicit function rule mc019-1.jpg.
a.
–1, 2, 8, 26, 80
c.
1, 2, 3, 4, 5
b.
2, 8, 26, 80, 242
d.
1, 3, 9, 27, 81
 

 20. 
Find the first five terms of the sequence recursively defined as the function with mc020-1.jpg.
a.
–10, –7, –4, –1, 2
b.
–10, –13, –16, –19, –22
c.
–13, –16, –19, –22, –25
d.
–10, 30, –90, 270, –810
 

Short Answer
 

 1. 
Write a recursive rule for the sequence.
sa001-1.jpg
 

 2. 
For a science experiment, Abdullah measures a bean stalk as it grows. In the first 4 weeks, he measures the stalk as 3, 6, 9, and 12 centimeters. Write an explicit rule for the height of the bean stalk in centimeters after n weeks.
 

 3. 
Mandy is adding ice cubes to her soup to cool it down. For the first 3 minutes after the soup is served, the temperature, in degrees Fahrenheit, is 150, 146.5, 143. Write a possible explicit rule for the temperature in the nth minute.
 

 4. 
Write the next three terms of the arithmetic sequence. Then write a variable expression for the nth term and evaluate it forsa004-1.jpg
sa004-2.jpg
 

 5. 
Write a rule for the nth term of the arithmetic sequence. –12, –5, 2, 9, . . .
 

 6. 
Write a rule for the nth term of the arithmetic sequence.
16, 19, 22, . . .
 

 7. 
Write a rule for the nth term of the arithmetic sequence with sa007-1.jpg and the common difference of sa007-2.jpg.
 

 8. 
Write a rule for the nth term of the arithmetic sequence with sa008-1.jpg and the common difference of sa008-2.jpg.
 

 9. 
Write a rule for the nth term of the arithmetic sequence with sa009-1.jpg and the common difference of sa009-2.jpg.
 

 10. 
Write the first five terms of the sequence. sa010-1.jpg;  sa010-2.jpg
 

 11. 
Write the first five terms of the sequence. sa011-1.jpg;  sa011-2.jpg
 

 12. 
Write a recursive rule for the sequence.
sa012-1.jpg
 

 13. 
The first step on a staircase is 24.5 centimeters high, and each step after the first is 23.5 centimeters high.
a.      Write a recursive rule that represents the height sa013-1.jpg, in centimeters, of the sa013-2.jpg step above the base of the staircase, where h(1) is the first term of the sequence.



b.      Write an explicit rule that represents the height sa013-3.jpg, in centimeters, of the sa013-4.jpg step above the base of the staircase.
 

 14. 
Calvin is practicing the trumpet for an audition to play in a band. He starts practicing the trumpet 40 minutes the first day and then increases his practice time by 5 minutes per day. The audition is on the 10th day.
a.      Write a recursive rule that represents the time sa014-1.jpg, in minutes, Calvin practices on day d.
b.      Write an explicit rule that represents the time sa014-2.jpg, in minutes, Calvin practices on day d.
c.      Use the result from part b to find how long Calvin practices on the 8th day. Show your work.
 

Problem
 

 1. 
Consider the sequence pr001-1.jpg
a.      Write a function describing the sequence whose domain is the set of consecutive integers starting with 1.



b.      Write a recursive function describing the sequence.



c.      Which of the functions from parts a and b would be easier to use to find the 50th term of the sequence? Explain.



d.      What is the 50th term of the sequence?
 



 
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