Lesson 4.1 Skills Practice
Name
Date
Is There a Pattern Here?
Recognizing Patterns and Sequences
Vocabulary
Choose the term that best completes each statement.
sequence
term of a sequence
infinite sequence
finite sequence
finite sequence .
1. A sequence which terminates is called a(n)
2. A(n) term of a sequence is an individual number, figure, or letter in a sequence.
sequence
3. A(n)
is a pattern involving an ordered arrangement of numbers, geometric
figures, letters, or other objects.
4. A sequence which continues forever is called a(n) infinite sequence .
Problem Set
4
Describe each given pattern. Draw the next two figures in each pattern.
1.
© 2012 Carnegie Learning
The second figure has 2 more squares than the first, the third figure has 3 more squares than the
second, and the fourth figure has 4 more squares than the third.
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Lesson 4.1 Skills Practice
page 2
2.
Each figure has 3 more line segments than the previous figure.
3.
Each figure has 2 more circles than the previous figure.
4
4.
5.
Each figure has twice as many triangles as the previous figure.
334 © 2012 Carnegie Learning
The second figure has 9 blocks less than the first figure and the third figure has 7 blocks less than
the second figure. The number of blocks being removed from one figure to the next decreases by
2 each time.
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Lesson 4.1 Skills Practice
Name
page 3
Date
6.
The second figure has 1 less square than the first, the third figure has 3 less squares than the
second, and the fourth figure has 5 less squares than the third. The number of squares being
removed from one figure to the next starts at 1 and then increases to the next larger odd integer
each time.
4
Write a numeric sequence to represent each given pattern or situation.
© 2012 Carnegie Learning
7. The school cafeteria begins the day with a supply of 1000 chicken nuggets. Each student that passes
through the lunch line is given 5 chicken nuggets. Write a numeric sequence to represent the total
number of chicken nuggets remaining in the cafeteria’s supply after each of the first 6 students pass
through the line. Include the number of chicken nuggets the cafeteria started with.
1000, 995, 990, 985, 980, 975, 970
8. Write a numeric sequence to represent the number of squares in each of the first 7 figures
of the pattern.
1, 3, 6, 10, 15, 21, 28
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Lesson 4.1 Skills Practice
page 4
9. Sophia starts a job at a restaurant. She deposits $40 from each paycheck into her savings account.
There was no money in the account prior to her first deposit. Write a numeric sequence to represent
the amount of money in the savings account after Sophia receives each of her first 6 paychecks.
$40, $80, $120, $160, $200, $240
10. Write a numeric sequence to represent the number of blocks in each of the first 5 figures
of the pattern.
25, 16, 9, 4, 1
11. Kyle is collecting canned goods for a food drive. On the first day he collects 1 can. On the second
day he collects 2 cans. On the third day he collects 4 cans. On each successive day, he collects
twice as many cans as he collected the previous day. Write a numeric sequence to represent the
total number of cans Kyle has collected by the end of each of the first 7 days of the food drive.
4
1, 3, 7, 15, 31, 63, 127
3, 6, 9, 12, 15, 18, 21
13. For her 10th birthday, Tameka’s grandparents give her a set of 200 stamps. For each birthday after
that, they give her a set of 25 stamps to add to her stamp collection. Write a numeric sequence
consisting of 7 terms to represent the number of stamps in Tameka’s collection after each of her
birthdays starting with her 10th birthday.
© 2012 Carnegie Learning
12. Write a numeric sequence to represent the number of line segments in each of the first 7 figures
of the pattern.
200, 225, 250, 275, 300, 325, 350
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Lesson 4.1 Skills Practice
Name
page 5
Date
14. Write a numeric sequence to represent the number of squares in each of the first 6 figures
of the pattern.
36, 35, 32, 27, 20, 11
15. Leonardo uses 3 cups of flour in each cake he bakes. He starts the day with 50 cups of flour.
Write a numeric sequence to represent the amount of flour remaining after each of the first 7 cakes
Leonardo bakes. Include the amount of flour Leonardo started with.
4
50, 47, 44, 41, 38, 35, 32, 29
© 2012 Carnegie Learning
16. Write a numeric sequence to represent the number of triangles in each of the first 7 figures
of the pattern.
1, 2, 4, 8, 16, 32, 64
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© 2012 Carnegie Learning
4
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Lesson 4.2 Skills Practice
Name
Date
The Password Is . . . Operations!
Arithmetic and Geometric Sequences
Vocabulary
Describe each given sequence using the terms arithmetic sequence, common difference, geometric
sequence, and common ratio as they apply.
1. 10, 20, 30, 40, . . .
This sequence is an arithmetic sequence because the difference between any two consecutive
terms is a constant. In this sequence, the common difference is 10.
2. 1, 2, 4, 8, . . .
This sequence is a geometric sequence because the ratio between any two consecutive terms
is a constant. In this sequence, the common ratio is 2.
4
Problem Set
Determine the common difference for each arithmetic sequence.
1. 1, 5, 9, 13, . . .
d5521
d 5 3 2 10
d54
d 5 27
3. 10.5, 13, 15.5, 18, . . .
© 2012 Carnegie Learning
2. 10, 3, 24, 211, . . .
d 5 13 2 10.5
d 5 2.5
​ 2 ​ , 1, __
4. __
​ 1 ​ , __
​ 4 ​ , . . .
3
3 3
2
d 5 ​    ​2 ​ 1  ​
3 3
__  __ 
__ 
d 5 ​ 1 ​ 
3
5. 95, 91.5, 88, 84.5, . . .
6. 170, 240, 310, 380, . . .
d 5 91.5 2 95
d 5 240 2 170
d 5 23.5
d 5 70
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Lesson 4.2 Skills Practice
7. 1250, 1190, 1130, 1070, . . .
page 2
8. 24.8, 26.0, 27.2, 28.4, . . .
d 5 1190 2 1250
d 5 26.0 2 (24.8)
d 5 260
d 5 21.2
1 ​ , 9, 9​ __
1 ​ , 10, . . .
9. 8​ __
2
2
d 5 9 2 8​ 1 ​ 
2
__ 
__ 
d 5 ​ 1 ​ 
10. 228, 213, 2, 17, . . .
d 5 213 2 (228)
d 5 15
2
Determine the common ratio for each geometric sequence.
4
r 5 10 4 5
r5842
r52
r54
13. 3, 26, 12, 224, . . .
r 5 26 4 3
r 5 22
15. 10, 230, 90, 2270, . . .
14. 800, 400, 200, 100, . . .
r 5 400 4 800
__ 
2
r 5 ​ 1 ​ 
16. 64, 232, 16, 28, . . .
r 5 230 4 10
r 5 232 4 64
r 5 23
r 5 2​ 1 ​ 
17. 5, 40, 320, 2560, . . .
r 5 40 4 5
r58
19. 0.2, 21, 5, 225, . . .
340 12. 2, 8, 32, 128, . . .
__ 
2
18. 45, 15, 5, __
​ 5 ​ , . . .
3
r 5 15 4 45
__1 
r 5 ​ 3 ​ 
20. 150, 30, 6, 1.2, . . .
r 5 21 4 0.2
r 5 30 4 150
r 5 25
r 5 ​ 1 ​ 
© 2012 Carnegie Learning
11. 5, 10, 20, 40, . . .
__ 
5
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Lesson 4.2 Skills Practice
page 3
Name
Date
Determine the next 3 terms in each arithmetic sequence.
21. 8, 14, 20, 26,
32 ,
30 ,
22. 90, 75, 60, 45,
38 ,
44 , . . .
15 ,
0
,...
23. 224, 214, 24, 6, 16 , 26 , 36 , . . .
​ 7 ​ 
​ 8 ​ 
​ 9 ​ 
3
6
4
__
__
__
5
5
24. ​    ​, ​   ​ , 1, ​   ​ ,
,
, 5 ,...
5
5 5
25. 20, 11, 2, 27, 216 , 225 , 234 , . . .
__ 
__ 
26. 12, 16.5, 21, 25.5,
__ 
30 , 34.5 ,
39 , . . .
27. 2101, 2112, 2123, 2134, 2145 , 2156 , 2167 , . . .
28. 3.8, 5.1, 6.4, 7.7,
9.0 , 10.3 , 11.6 , . . .
29. 2500, 2125, 250, 625, 1000 , 1375 , 1750 , . . .
30. 24.5, 20.7, 16.9, 13.1,
9.3 ,
5.5 ,
4
1.7 , . . .
Determine the next 3 terms in each geometric sequence.
31. 3, 9, 27, 81, 243 , 729 , 2187 , . . .
© 2012 Carnegie Learning
32. 512, 256, 128, 64,
32 ,
16 ,
8
,...
33. 5, 210, 20, 240,
80 , 2160 , 320 , . . .
34. 3000, 300, 30, 3,
0.3 , 0.03 , 0.003 , . . .
35. 2, 22, 2, 22,
2
,
22 ,
2
,...
36. 0.2, 1.2, 7.2, 43.2, 259.2 , 1555.2 , 9331.2 , . . .
37. 28000, 4000, 22000, 1000, 2500 , 250 , 2125 , . . .
38. 0.1, 0.4, 1.6, 6.4, 25.6 , 102.4 , 409.6 , . . .
39. 156.25, 31.25, 6.25, 1.25, 0.25 , 0.05 , 0.01 , . . .
40. 7, 221, 63, 2189, 567 , 21701 , 5103 , . . .
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Lesson 4.2 Skills Practice
page 4
Determine whether each given sequence is arithmetic, geometric, or neither. For arithmetic and geometric
sequences, write the next 3 terms of the sequence.
41. 4, 8, 12, 16, . . .
The sequence is arithmetic. The next 3 terms are 20, 24, and 28.
42. 2, 4, 7, 11, . . .
The sequence is neither arithmetic nor geometric.
43. 3, 12, 48, 192, . . .
The sequence is geometric. The next 3 terms are 768, 3072, and 12,288.
44. 9, 218, 36, 272, . . .
The sequence is geometric. The next 3 terms are 144, 2288, and 576.
45. 1.1, 1.11, 1.111, 1.1111, . . .
The sequence is neither arithmetic nor geometric.
4
46. 4, 28, 220, 232, . . .
The sequence is arithmetic. The next 3 terms are 244, 256, and 268.
47. 7.5, 11.6, 15.7, 19.8, . . .
The sequence is arithmetic. The next 3 terms are 23.9, 28.0, and 32.1.
48. 1, 24, 9, 216, . . .
49. 5, 220, 80, 2320, . . .
The sequence is geometric. The next 3 terms are 1280, 25120, and 20,480.
50. 9.8, 5.6, 1.4, 22.8, . . .
The sequence is arithmetic. The next 3 terms are 27.0, 211.2, and 215.4.
342 © 2012 Carnegie Learning
The sequence is neither arithmetic nor geometric.
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Lesson 4.3 Skills Practice
Name
Date
The Power of Algebra Is a Curious Thing
Using Formulas to Determine Terms of a Sequence
Vocabulary
Choose the term that best completes each statement.
index
explicit formula
recursive formula
1. A(n) recursive formula expresses each term of a sequence based on the preceding term
of the sequence.
index
2. The
is the position of a term in a sequence.
3. A(n) explicit formula calculates each term of a sequence using the term’s position
in the sequence.
Problem Set
4
Determine each unknown term in the given arithmetic sequence using the explicit formula.
1. Determine the 20th term of the sequence
1, 4, 7, . . .
© 2012 Carnegie Learning
an 5 a1 1 d(n 2 1)
2. Determine the 30th term of the sequence
210, 215, 220, . . .
an 5 a1 1 d(n 2 1)
a20 5 1 1 3(20 2 1)
a30 5 210 1 (25)(30 2 1)
a20 5 1 1 3(19)
a30 5 210 1 (25)(29)
a20 5 1 1 57
a30 5 210 1 (2145)
a20 5 58
a30 5 2155
3. Determine the 25th term of the sequence
3.3, 4.4, 5.5, . . .
an 5 a1 1 d(n 2 1)
4. Determine the 50th term of the sequence
100, 92, 84, . . .
an 5 a1 1 d(n 2 1)
a25 5 3.3 1 1.1(25 2 1)
a50 5 100 1 (28)(50 2 1)
a25 5 3.3 1 1.1(24)
a50 5 100 1 (28)(49)
a25 5 3.3 1 26.4
a50 5 100 1 (2392)
a25 5 29.7
a50 5 2292
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Lesson 4.3 Skills Practice
an 5 a1 1 d(n 2 1)
an 5 a1 1 d(n 2 1)
a42 5 12.25 1 2.25(42 2 1)
a28 5 2242 1 (29)(28 2 1)
a42 5 12.25 1 2.25(41)
a28 5 2242 1 (29)(27)
a42 5 12.25 1 92.25
a28 5 2242 1 (2243)
a42 5 104.50
a28 5 2485
7. Determine the 34th term of the sequence
276.2, 270.9, 265.6, . . .
an 5 a1 1 d(n 2 1)
4
6. Determine the 28th term of the sequence
–242, –251, –260, . . .
8. Determine the 60th term of the sequence
10, 25, 40, . . .
an 5 a1 1 d(n 2 1)
a34 5 276.2 1 5.3(34 2 1)
a60 5 10 1 15(60 2 1)
a34 5 276.2 1 5.3(33)
a60 5 10 1 15(59)
a34 5 276.2 1 174.9
a60 5 10 1 885
a34 5 98.7
a60 5 895
9. Determine the 57th term of the sequence
672, 660, 648, . . .
an 5 a1 1 d(n 2 1)
10. Determine the 75th term of the sequence
2200, 2100, 0, . . .
an 5 a1 1 d(n 2 1)
a57 5 672 1 (212)(57 2 1)
a75 5 2200 1 100(75 2 1)
a57 5 672 1 (212)(56)
a75 5 2200 1 100(74)
a57 5 672 1 (2672)
a75 5 2200 1 7400
a57 5 0
a75 5 7200
Determine each unknown term in the given geometric sequence using the explicit formula. Round the
answer to the nearest hundredth when necessary.
11. Determine the 10th term of the sequence
3, 6, 12, . . .
​ ​
gn 5 g1 ? ​r n21
344 12. Determine the 15th term of the sequence
1, 22, 4, . . .
gn 5 g1 ? ​r ​n21​
g10 5 3 ? ​21021
​ ​
g15 5 1 ? (22​)1521
​ ​
g10 5 3 ? ​29​ ​
g15 5 1 ? (22​)14
​​
g10 5 3 ? 512
g15 5 1 ? 16,384
g10 5 1536
g15 5 16,384
© 2012 Carnegie Learning
5. Determine the 42nd term of the sequence
12.25, 14.50, 16.75, . . .
page 2
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Lesson 4.3 Skills Practice
page 3
Name
13. Determine the 12th term of the sequence
5, 15, 45, . . .
14. Determine the 16th term of the sequence
9, 18, 36, . . .
gn 5 g1 ? ​r ​n21​
gn 5 g1 ? ​r ​n21​
g12 5 5 ? ​31221
​ ​
g16 5 9 ? ​21621
​ ​
g12 5 5 ? ​311
​​
g16 5 9 ? ​215
​​
g12 5 5 ? 177,147
g16 5 9 ? 32,768
g12 5 885,735
g16 5 294,912
15. Determine the 20th term of the sequence
0.125, 20.250, 0.500, . . .
gn 5 g1 ? ​r ​n21​
16. Determine the 18th term of the sequence
3, 9, 27, . . .
gn 5 g1 ? ​r ​n21​
g20 5 0.125 ? (22​)2021
​ ​
g18 5 3 ? ​31821
​ ​
g20 5 0.125 ? (22​)19
​​
g18 5 3 ? ​317
​​
g20 5 0.125 ? (2524,288)
g18 5 3 ? 129,140,163
g20 5 265,536
g18 5 387,420,489
17. Determine the 14th term of the sequence
24, 8, 216, . . .
gn 5 g1 ? ​r ​n21​
© 2012 Carnegie Learning
Date
18. Determine the 10th term of the sequence
0.1, 0.5, 2.5, . . .
gn 5 g1 ? ​r ​n21​
g14 5 24 ? (22​)1421
​ ​
g10 5 0.1 ? ​51021
​ ​
g14 5 24 ? (22​)13
​​
g10 5 0.1 ? ​59​ ​
g14 5 24 ? (28192)
g10 5 0.1 ? 1,953,125
g14 5 32,768
g10 5 195,312.5
19. Determine the 12th term of the sequence
4, 5, 6.25, . . .
gn 5 g1 ? ​r ​n21​
20. Determine the 10th term of the sequence
5, 225, 125, . . .
gn 5 g1 ? ​r ​n21​
g12 5 4 ? ​1.25​1221​
g10 5 5 ? (25​)1021
​ ​
g12 5 4 ? ​1.25​11​
g10 5 5 ? (25​)9​ ​
g12 ¯ 4 ? 11.6415
g10 5 5 ? (21,953,125)
g12 ¯ 46.57
g10 5 29,765,625
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 345
4
345
20/04/12 11:30 AM
Lesson 4.3 Skills Practice
page 4
Determine whether each sequence is arithmetic or geometric. Then, use the appropriate recursive formula
to determine the unknown term(s) in the sequence.
64
21. 4, 8, 16, 32,
,...
The sequence is geometric.
gn 5 gn21 ? r
g5 5 g4 ? 2
g5 5 32 ? 2
g5 5 64
72
22. 16, 30, 44, 58,
,...
The sequence is arithmetic.
an 5 an21 1 d
a5 5 a4 1 14
a5 5 58 1 14
a5 5 72
4
23. 2, 26, 18,
254
, 162,
2486
,...
The sequence is geometric.
gn 5 gn21 ? r
gn 5 gn21 ? r
g4 5 g3 ? (23)
g6 5 g5 ? (23)
g4 5 18 ? (23)
g6 5 162 ? (23)
g4 5 254
g6 5 2486
24. 7.3, 9.4, 11.5,
13.6
, 15.7,
17.8
,...
an 5 an21 1 d
an 5 an21 1 d
a4 5 a3 1 2.1
a6 5 a5 1 2.1
a4 5 11.5 1 2.1
a6 5 15.7 1 2.1
a4 5 13.6
a6 5 17.8
25. 320, 410, 500,
590
,
680
,...
The sequence is arithmetic.
346 an 5 an21 1 d
an 5 an21 1 d
a4 5 a3 1 90
a5 5 a4 1 90
a4 5 500 1 90
a5 5 590 1 90
a4 5 590
a5 5 680
© 2012 Carnegie Learning
The sequence is arithmetic.
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Lesson 4.3 Skills Practice
page 5
Name
26. 7, 21, 63,
Date
189
1701
, 567,
,...
The sequence is geometric.
gn 5 gn21 ? r
gn 5 gn21 ? r
g4 5 g3 ? 3
g6 5 g5 ? 3
g4 5 63 ? 3
g6 5 567 ? 3
g4 5 189
g6 5 1701
2113
27. 268, 283, 298,
,
2128
,
2143
,...
The sequence is arithmetic.
an 5 an21 1 d
an 5 an21 1 d
an 5 an21 1 d
a4 5 a3 1 (215)
a5 5 a4 1 (215)
a6 5 a5 1 (215)
a4 5 298 1 (215)
a5 5 2113 1 (215)
a6 5 2128 1 (215)
a4 5 2113
a5 5 2128
a6 5 2143
28. 25, 20, 280,
320
,
21280 ,
5120
4
,...
The sequence is geometric.
gn 5 gn21 ? r
gn 5 gn21 ? r
gn 5 gn21 ? r
g4 5 g3 ? (24)
g5 5 g4 ? (24)
g6 5 g5 ? (24)
g4 5 280 ? (24)
g5 5 320 ? (24)
g6 5 21280 ? (24)
g4 5 320
g5 5 21280
g6 5 5120
© 2012 Carnegie Learning
Determine the unknown term in each arithmetic sequence using a graphing calculator.
29. Determine the 20th term of the sequence
30, 70, 110, . . .
a20 5 790
31. Determine the 30th term of the sequence
16, 24, 32, . . .
a30 5 248
30. Determine the 25th term of the sequence
225, 250, 275, . . .
a25 5 2625
32. Determine the 35th term of the sequence
120, 104, 88, . . .
a35 5 2424
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 347
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Lesson 4.3 Skills Practice
33. Determine the 30th term of the sequence
350, 700, 1050, . . .
a30 5 10,500
35. Determine the 24th term of the sequence
6.8, 9.5, 12.2, . . .
a24 5 68.9
37. Determine the 20th term of the sequence
2500, 3100, 3700, . . .
a20 5 13,900
page 6
34. Determine the 22nd term of the sequence
0, 245, 290, . . .
a22 5 2945
36. Determine the 36th term of the sequence
189, 200, 211, . . .
a36 5 574
38. Determine the 50th term of the sequence
297, 294, 291, . . .
a50 5 50
© 2012 Carnegie Learning
4
348 Chapter 4 Skills Practice
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Lesson 4.4 Skills Practice
Name
Date
Thank Goodness Descartes Didn’t Drink Some Warm Milk!
Graphs of Sequences
Problem Set
Complete the table for each given sequence then graph each sequence on the coordinate plane.
1. an 5 15 1 3(n 2 1)
y
Value of Term (an)
1
15
45
2
18
40
3
21
4
24
5
27
6
30
7
33
8
36
5
9
39
0
10
42
Value of Term (an)
Term Number (n)
35
30
25
20
4
15
10
1
2
3 4 5 6 7 8
Term Number (n)
9
1
2
3 4 5 6 7 8
Term Number (n)
9
x
y
Term Number (n)
Value of Term (gn)
1
3
1800
2
6
1600
3
12
4
24
5
48
6
96
7
192
8
384
200
9
768
0
10
1536
Value of Term (gn)
© 2012 Carnegie Learning
2. gn 5 3 ? ​2n21
​ ​
1400
1200
1000
800
600
400
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 349
x
349
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Lesson 4.4 Skills Practice
page 2
3. an 5 50 1 (28)(n 2 1)
4
y
Value of Term (an)
1
50
50
2
42
40
3
34
4
26
5
18
6
10
7
2
8
26
9
214
10
222
Value of Term (an)
Term Number (n)
30
20
10
0
1
210
2
3
4
5
6
7
8
9
8
9
x
220
230
Term Number (n)
4. gn 5 3 ? (22​)n21
​ ​
350 y
Value of Term (gn)
1
3
600
2
26
300
3
12
4
224
5
48
6
296
7
192
8
2384
9
768
10
21536
0
2300
1
2
3
4
5
6
7
x
2600
2900
21200
21500
21800
Term Number (n)
© 2012 Carnegie Learning
Value of Term (gn)
Term Number (n)
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Lesson 4.4 Skills Practice
page 3
Name
Date
5. an 5 224 1 6(n 2 1)
y
Value of Term (an)
1
224
30
2
218
24
3
212
4
26
5
0
6
6
7
12
8
18
9
24
10
30
Value of Term (an)
Term Number (n)
18
12
6
0
1
26
2
3
4
5
6
7
8
9
x
212
218
Term Number (n)
4
y
Term Number (n)
Value of Term (gn)
1
21
0
2
22
260
3
24
4
28
5
216
6
232
7
264
8
2128
9
2256
10
2512
Value of Term (gn)
© 2012 Carnegie Learning
6. gn 5 21 ? ​2n21
​ ​
1
2
3
4
5
6
7
8
9
2120
2180
2240
2300
2360
2420
2480
Term Number (n)
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 351
x
351
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Lesson 4.4 Skills Practice
page 4
7. an 5 75 1 25(n 2 1)
4
y
Value of Term (an)
1
75
450
2
100
400
3
125
4
150
5
175
6
200
7
225
8
250
50
9
275
0
10
300
Value of Term (an)
Term Number (n)
350
300
250
200
150
100
1
2
3 4 5 6 7 8
Term Number (n)
9
1
2
3 4 5 6 7 8
Term Number (n)
9
x
8. gn 5 32,000 ? (0.5​)n21
​ ​
352 y
Value of Term (gn)
1
32,000
36,000
2
16,000
32,000
3
8000
4
4000
5
2000
6
1000
7
500
8
250
4,000
9
125
0
10
62.5
28,000
24,000
20,000
16,000
12,000
8,000
x
© 2012 Carnegie Learning
Value of Term (gn)
Term Number (n)
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Lesson 4.4 Skills Practice
page 5
Name
Date
9. an 5 400 1 (280)(n 2 1)
y
Value of Term (an)
1
400
400
2
320
320
3
240
4
160
5
80
6
0
7
280
8
2160
9
2240
10
2320
Value of Term (an)
Term Number (n)
240
160
80
0
1
280
2
3
4
5
6
7
8
9
x
2160
2240
Term Number (n)
4
Term Number (n)
Value of Term (gn)
1
2
2
26
3
18
4
254
5
162
6
2486
7
1458
8
24374
9
13,122
10
239,366
y
12,000
6000
Value of Term (gn)
© 2012 Carnegie Learning
10. gn 5 2 ? (23​)n21
​ ​
0
26000
1
2
3
4
5
6
7
8
9
212,000
218,000
224,000
230,000
236,000
Term Number (n)
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 353
x
353
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© 2012 Carnegie Learning
4
354 Chapter 4 Skills Practice
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Lesson 4.5 Skills Practice
Name
Date
Well, Maybe It Is a Function!
Sequences and Functions
Problem Set
Write each arithmetic sequence as a linear function. Graph the function for all integers, n, such that
1 # n # 10.
1. an 5 16 1 5(n 2 1)
an 5 16 1 5(n 2 1)
f(n) 5 16 1 5(n 2 1)
f(n) 5 16 1 5n 2 5
f(n) 5 5n 1 16 2 5
f(n) 5 5n 1 11
y
90
80
70
60
50
40
4
30
20
10
0
2. an 5 250 1 15(n 2 1)
an 5 250 1 15(n 2 1)
© 2012 Carnegie Learning
f(n) 5 250 1 15(n 2 1)
f(n) 5 250 1 15n 2 15
f(n) 5 15n 2 50 2 15
f(n) 5 15n 2 65
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
y
75
60
45
30
15
0
215
x
230
245
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 355
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Lesson 4.5 Skills Practice
page 2
3. an 5 100 1 (220)(n 2 1)
an 5 100 1 (220)(n 2 1)
f(n) 5 100 1 (220)(n 2 1)
f(n) 5 100 2 20n 1 20
f(n) 5 220n 1 100 1 20
f(n) 5 220n 1 120
y
80
60
40
20
0
220
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
240
260
280
4. an 5 29 1 (27)(n 2 1)
an 5 29 1 (27)(n 2 1)
f(n) 5 29 1 (27)(n 2 1)
4
y
0
f(n) 5 29 2 7n 1 7
210
f(n) 5 27n 2 9 1 7
220
f(n) 5 27n 2 2
230
x
240
250
260
270
280
5. an 5 550 1 (250)(n 2 1)
f(n) 5 550 1 (250)(n 2 1)
f(n) 5 550 2 50n 1 50
f(n) 5 250n 1 500 1 50
f(n) 5 250n 1 600
© 2012 Carnegie Learning
an 5 550 1 (250)(n 2 1)
y
540
480
420
360
300
240
180
120
60
0
356 x
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Lesson 4.5 Skills Practice
page 3
Name
Date
(  )
(  __ )
__3
f(n) 5 3 1 ​( 2​   ​   )​(n 2 1)
5
3
__
f(n) 5 3 2 ​    ​n
  1 __​ 53 ​  
5
__3  1 3 1 __​ 3 ​  
f(n) 5 2​    ​n
5
5
3
__
f(n) 5 2​    ​n
  1 ___
​ 18 ​  
5
5
3
6. an 5 3 1 ​2__
​   ​   ​(n 2 1)
5
3
an 5 3 1 ​ 2​   ​   ​(n 2 1)
5
y
4
3
2
1
0
1
21
2
3
4
5
6
7
8
9
x
22
23
24
4
Write each geometric sequence as an exponential function. Graph the function for all integers, n, such that
1 # n # 10.
7. gn 5 5 ? 2n 2 1
gn 5 5 ? 2
y
n 21
f(n) 5 5 ? 2n 21
f(n) 5 5 ? 2n ? 221
f(n) 5 5 ? 221 ? 2n
f(n) 5 5 ? ​ 1 ​ ? 2n
2
f(n) 5 ​ 5 ​ ? 2n
2
© 2012 Carnegie Learning
__ 
__ 
2700
2400
2100
1800
1500
1200
900
600
300
0
1
2
3
4
5
6
7
8
9
x
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 357
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Lesson 4.5 Skills Practice
page 4
8. gn 5 23 ? 3n 2 1
gn 5 23 ? 3n 2 1
f(n) 5 23 ? 3n 2 1
y
0
f(n) 5 23 ? 3n ? 321
210,000
f(n) 5 23 ? 321 ? 3n
f(n) 5 23 ? ​ 1 ​ ? 3n
3
3
f(n) 5 2​   ​ ? 3n
3
f(n) 5 21 ? 3n
220,000
__ 
__ 
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
230,000
240,000
250,000
260,000
270,000
280,000
9. gn 5 20 ? 2.5n 2 1
gn 5 20 ? 2.5
y
n21
f(n) 5 20 ? 2.5n 2 1
f(n) 5 20 ? 2.5n ? 2.521
f(n) 5 20 ? 2.521 ? 2.5n
4
___ 
f(n) 5 20 ? ​  1   ​? 2.5n
2.5
20
f(n) 5 ​    ​? 2.5n
2.5
f(n) 5 8 ? 2.5n
___ 
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
10. gn 5 900 ? 0.9n 2 1
f(n) 5 900 ? 0.9n 2 1
f(n) 5 900 ? 0.9n ? 0.921
f(n) 5 900 ? 0.921 ? 0.9n
___ 
f(n) 5 900 ? ​  1   ​? 0.9n
0.9
f(n) 5 ​ 900 ​ ? 0.9n
0.9
f(n) 5 1000 ? 0.9n
____ 
y
900
© 2012 Carnegie Learning
gn 5 900 ? 0.9n 2 1
x
800
700
600
500
400
300
200
100
0
358 x
Chapter 4 Skills Practice
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Lesson 4.5 Skills Practice
page 5
Name
Date
11. gn 5 20.5 ? 2n 2 1
y
gn 5 20.5 ? 2n 2 1
f(n) 5 20.5 ? 2n 2 1
0
f(n) 5 20.5 ? 2n ? 221
230
f(n) 5 20.5 ? 221 ? 2n
260
f(n) 5 20.5 ? ​ 1 ​ ? 2n
2
20.5
? 2n
f(n) 5 ​   ​ 
2
f(n) 5 20.25 ? 2n
290
_____ 
__ 
1
2
3
4
5
6
7
8
9
x
2120
2150
2180
2210
2240
12. gn 5 1250 ? 1.25n 2 1
gn 5 1250 ? 1.25
4
y
n21
f(n) 5 1250 ? 1.25n 2 1
f(n) 5 1250 ? 1.25n ? 1.2521
f(n) 5 1250 ? 1.2521 ? 1.25n
_____ 
f(n) 5 1250 ? ​  1   ​? 1.25n
1.25
f(n) 5 ​ 1250 ​ 
? 1.25n
1.25
f(n) 5 1000 ? 1.25n
_____ 
9000
8000
7000
6000
5000
4000
3000
© 2012 Carnegie Learning
2000
1000
0
1
2
3
4
5
6
7
8
9
x
Chapter 4 Skills Practice 8045_Skills_Ch04.indd 359
359
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© 2012 Carnegie Learning
4
360 Chapter 4 Skills Practice
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