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Geometry 1A
Name _____________________
Homework
1.1
Find and describe a pattern for each sequence. Use the pattern to show the next two
terms.
1. 5, 10, 20, 40, _____, ______
2. 1, -1, 2, -2, 3, _____, ______
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
3. 15, 12, 9, 6, _____, ______
4. 1,
1 1 1
1
, ,
,
, _____, ______
4 9 16 25
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
5. 81, 27, 9, 3, _____, ______
6. 1, 2, 6, 24, 120, _____, ______
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
7. 1, 2, 5, 6, 9, _____, ______
8. 0,
1 3 7 15
, , ,
, _____, ______
2 4 8 16
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
Draw the next figure in each sequence.
9.
10.
11.
12.
13.
14.
Use the table and inductive reasoning. Make a conjecture about each value.
15. The sum of the first 6 positive
even numbers.
2
=2
2+4
=6
2+4+6
= 12
2+4+6+8
= 20
16. The sum of the first 30 positive
2 + 4 + 6 + 8 + 10 = 30
even numbers.
17. The sum of the first 100 positive even numbers.
=1•2
=2•3
=3•4
=4•5
=5•6
Find one counterexample to show that each conjecture is false.
18. The sum of two numbers is greater than either number.
19. The product of two positive numbers is greater than either number.
20. The difference of two integers is less than either integer.
21. The quotient of two proper fractions is a proper fraction.
22. Use inductive reasoning to find the perimeter when 100 triangles are put together in
the pattern shown below. Assume that all triangle sides are 1 cm long.
23. Leonardo of Pisa (about 1175-1258), also known as Fibonacci, was born in Italy
and educated in North Africa. He was one of the first Europeans known to use
modern numerals instead of Roman numerals. The special sequence 1, 1, 2, 3, 5,
8, 13, …. is known as the Fibonacci sequence. Find the next three terms of this
sequence.
Answer Key
1. 80 , 160
2. – 3, 4
3. 3, 0
1 1
4.
,
36 49
1
5. 1,
3
6. 720, 5040
7. 10, 13
31 63
8.
,
32 64
9.
10.
11.
12.
13.
14.
15. 6 g 7 = 42
16. 30 g 31 = 930
17. 100 g 101 = 10,100
18 – 21 Answers will vary:
18. 8 + (– 5) = 3, 3 < 8
1 1 1 1 1
19.
g = , <
2 3 6 6 2
20. – 6 – (– 4) = – 2
1 1 3
21.
g =
2 3 2
22. 102 cm
23. 21, 34, 55
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