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LESSON 2.1
Practice C
For use with pages 72–78
Sketch the next figure in the pattern.
1.
2.
Describe a pattern in the numbers. Write the next number in the pattern. Graph the
pattern on a number line.
3. –5, 7, –9, 11, –13,…
4. 22, 21, 19, 16, 12,…
5. 5.1, –6.2, 7.3, –8.4
6. 100, 101, 98, 103, 96, 105,…
7.
10 9 8 7
,
, , ,…
11 10 9 8
8. –
1 3 5 7
, ,–
,…
2 3 4 5
9. –1, 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,…
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Date ___________________
LESSON 2.1
Practice C Continued
For use with pages 72–78
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
Squares
First Differences
1
1
2
4
3
Second Differences
14.
15.
3
9
4
16
5
2
7
2
5
25
9
2
6
36
11
2
7
49
13
2
8
64
15
2
Conjecture For squares of consecutive natural numbers, each first difference is
__?__the previous first difference.
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 an even
number.
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,–3), (2,–4), (3,–5), (4,–6)
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
1
2
2 3
4
4
5
First Differences 2
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.