1. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
Pages 6–9 Exercises
1. 80, 160
2. 33,333; 333,333
3. –3, 4 ,
5. 3, 0
6. 1,
7. N, T
8. J, J
9. 720, 5040
10. 64, 128 , 1 16 32 36 49 ,
13. James, John
14. Elizabeth, Louisa
15. Andrew, Ulysses
16. Gemini, Cancer
17.
18. 5 6
19. The sum of the first 6 pos.
even numbers is
6 • 7, or 42.
20. The sum of the first 30 pos.
30 • 31, or 930.
21. The sum of the first 100
pos. even numbers is
100 • 101, or 10,100. 3
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2. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
31. 31, 43
32. 10, 13 ,
, 202
35. 63, 127 ,
37. J, S
38. CA, CO
39. B, C
÷ = and is
improper.
29. 75°F
push-ups;
answers may vary.
Sample: Not very
confident, Dino may
reach a limit to the
number of push-ups
he can do in his
allotted time for
exercises. 1 2 1 3 3 2 3 2
22. The sum of the first
100 odd numbers is
1002, or 10,000.
,555,555
,454,321
25–28. Answers may vary.
Samples are given.
(–5 = 3) and 3 > 8
• > and • >
27. –6 – (–4) < –6 and
–6 – (–4) < –4 31 32 63 64 / 1 3 1 2 1 3 1 3 1 2 1 2 / /
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3. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
40. Answers may vary.
Sample: In Exercise
31, each number
increases by increasing
multiples of 2. In Exercise
33, to get the next term,
divide by 10.
41.
You would get a third line
between and parallel to
the first two lines.
42.
43.
44.
45. cm
47. Answers may vary.
Samples are given.
a. Women may soon outrun
men in running competitions.
b. The conclusion was based
on continuing the trend
shown in past records.
c. The conclusions are
based on fairly recent
records for women,
and those rates of
improvement may not
continue. The conclusion
about the marathon is most
suspect because records
date only from 1955.
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4. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
48. a.
b. about 12,000 radio
stations in 2010
c. Answers may vary.
Sample: Confident;
the pattern has held
for several decades.
49. Answers may vary.
Sample: 1, 3, 9, 27,
81, . . .
1, 3, 5, 7, 9, . . .
52. 21, 34, 55
53. a. Leap years are years
that are divisible by 4.
b. 2020, 2100, and 2400
c. Leap years are years
divisible by 4, except
the final year of a
century which must
be divisible by 400.
So, 2100 will not be a
leap year, but 2400
will be.
50. His conjecture is
probably false
because most
people’s growth
slows by 18 until
they stop growing
somewhere between
18 and 22 years.
51. a.
b. H and I
c. a circle
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5. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
54. Answers may vary.
Sample: … … …
The sum of the first 100 numbers is
, or 5050.
The sum of the first n numbers is .
55. a. 1, 3, 6, 10, 15, 21
b. They are the same.
c. The diagram shows the product of n
and n + 1 divided by 2 when
n = 3. The result is 6.
100 • 101 2
n(n+1)
55. (continued) d.
56. B
57. I
58. [2] a. 25, 36, 49
b. n2
[1] one part correct
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6. Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
59. [4] a. The product of 11 and a three-digit number that begins and ends in 1 is a four-digit number that begins and ends in 1 and has middle digits that are each one greater than the middle digit of the three-digit number.
(151)(11) = 1661
(161)(11) = 1771
b. 1991
c. No; (191)(11) = 2101
59. (continued)
[3] minor error in explanation
[2] incorrect description
in part (a)
[1] correct products for (151)(11), (161)(11), and (181)(11)
60-67.
68. B
69. N
70. G
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