Download Practice C

Name———————————————————————— Lesson
2.1
Date —————————————
Practice C
For use with the lesson “Use Inductive Reasoning”
Sketch the next figure in the pattern.
1.
2.
Lesson 2.1
Describe a pattern in the numbers. Write the next number in the pattern.
Graph the pattern on a number line.
3. 25, 7, 29, 11, 213, . . .
4. 22, 21, 19, 16, 12, . . .
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5. 5.1, 26.2, 7.3, 28.4
6. 100, 101, 98, 103, 96, 105, . . .
5 7
1 3
8. 2​ } ​, }
​   ​, 2​ }4 ​, }
​ 5 ​, . . .
2 3
10 9 8 7
7.​ }
 ​,  }
​    ​,  }
​   ​, }
​   ​, . . .
11 10 9 8
9. 21, 1, 5, 13, 29, . . .
10. 1.1, 3.3, 13.2, 66, 396, . . .
Describe a pattern in the numbers and write the next three numbers in
the pattern. Then describe a different pattern in the numbers and write
the next three numbers in the pattern.
11. 1, 2, 4, . . .
12. 3, 6, 12, . . .
13. 1, 4, 8, . . .
Geometry
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Name———————————————————————— Date —————————————
Practice C continued
Lesson
2.1
For use with the lesson “Use Inductive Reasoning”
In Exercises 14 and 15, complete the conjecture based on the
pattern you observe in the table. The table shows the squares of
several natural numbers. The first differences are the differences
of consecutive squares. The second differences are the differences
of consecutive first differences.
Whole Numbers
1
2
3
4
5
6
7
8
Squares
1
4
9
16
25
36
49
64
First Differences
3
Lesson 2.1
Second Differences
5
7
2
2
9
2
11
2
13
2
15
2
14. Conjecture For squares of consecutive natural numbers, each first difference is
   ?    the previous first difference.
15. Conjecture For squares of consecutive natural numbers, each second difference
is    ?    the previous second difference.
Show the conjecture is false by finding a counterexample.
16. The sum of the squares of any two consecutive squared natural numbers is
17. The sum of the squares of any two squared natural numbers is an odd number.
For the given ordered pairs, write a function rule relating x and y.
18. (1, 23), (2, 24), (3, 25), (4, 26)
19. (1, 4), (2, 9), (3, 16), (4, 25)
20. Circumference A circular pond has a circumference of 280 feet. You are going to
install a fence around the pond, 7 feet from the water’s edge. You need to know how
much fencing to buy.
a. First, explore a pattern of the relationship between a circle’s radius and its
circumference by using the circumference formula to complete the
following table.
Radius
Circumference
First Differences
2-12
1
2
2π
4π
3
4
5
2π
b. Based on the table, make a conjecture about how the circumference of a
circle changes with each 1 unit increase in its radius.
c. Use your conjecture to determine the length of fencing you need to the
nearest foot.
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an even number.
Geometry
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Lesson 2.1 Use Inductive
Reasoning, continued
answers
19. y 5 x 3 20. y 5 2x 2 7 21. y 5 2x 1 5
1
22. y 5 }
​ x ​ 23. 512 billion bacteria 24. 15 days
Practice Level C
1.
2.
3. add 2 to the absolute value of the previous
number and use the opposite sign; 15;
213 29 25
213 29
25
3
21
7
11
15
7
11
15
11. Sample answer: double the previous number;
8, 16, 32; add n to the previous (nth) number;
7, 11, 16
12. Sample answer: double the previous number;
24, 48, 96; the nth number is (n 1 1)2 2 n; 21, 31,
43 13. Sample answer: the nth number is 2n; 16,
32, 64; add n 1 1 to the previous (nth) number;
13, 19, 26
14. 2 greater than 15. equal to
16. Sample answer: 12 1 22 5 5, 5 is not even
17. Sample answer: 12 1 32 5 10, 10 is not odd
18. Sample answer: y 5 22 2 x
19. Sample answer: y 5 (x 1 1)2
20. a.
4. subtract n from the previous (nth) number; 7;
7
0
2
4
6
12
16
19 21 22
8 10 12 14 16 18 20 22
5. add 1.1 to the absolute value of the previous
number and use the opposite sign; 9.5;
5.1 7.3 9.5
28.4 26.2
0
210 28 26 24 22
2
4
6
8 10
1
2
3
4
5
2π
4π
6π
8π
10π
2π
2π
2π
2π
b. conjecture: Each increase of 1 unit of the radius
increases the circumference by 2π units. c. 324 ft
Study Guide
1.
92
94
96
98 100 101103 105
94
96
98
100 102 104 106
7. subtract 1 from both the numerator and the
6
denominator of the previous number; ​ }7 ​;
6
7
7
8
8
9
9
10
10
11
0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92
8. add 1 to the denominator and 2 to the
numerator of the previous number and
9
3
change the sign; 2​ }6 ​5 2​ }2 ​;
3
5
1
22 24
22
22
1
0
21
7
5
1
2
n
9. add 2 to the previous (nth) number; 61;
21 1 5 13
210
0
10
29
20
30
61
40
50
60
70
10. multiply the previous (nth) number by
2500
A14
0
500
Real-Life Application
1. a. 11 b. 5 2. 55 3. 10 pairs of numbers
that sum to 21; 210 4. The sum of each pair
will be the same as the sum of the first and last
number. The total number of pairs will be half the
last number. Multiply the sum by the number of
n
pairs. Sum 5 (n 1 1) ​ }2 ​ 5. 5050
n
1
6. ​ } ​ (n 1 2); }
​ 4 ​the number of pairs and the sum
4
of each pair is n 1 2 instead of n 1 1.
Challenge Practice
(n 1 2); 2772
1.1 3.3 13.2 66 396
2. Each number is 4 more than the previous number; 17 3. Each number is 3 times the
previous number; 243 4. The product of any two
even integers is even. 5. The product of an even
integer and an odd integer is even.
6. Sample answer: 2 2 5 5 23, which is not
positive
2272
1000 1500 2000 2500
1. 27, 24, 21, 2, 5, 8, 11; Each number is three
more than the previous number.
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6. the nth number is 100 1 (21)n(n 2 1); 94;
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