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1SimpleNWierdSequences
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Inductive Reasoning
1 2 3 4 5 6 … n … 20
0 3 10 21 36 55 … ? … ?
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Sequences
Terms: 4, 5, 6, 7, 8 …
Terms: A, C, E, G, …
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2, 4, 6, 8, 10, ___, ____
Find the next 2 terms.
5, 10, 15, 20, 25, ___, ____
4, 8, 12, 16, 20, ___, ____
Add two to the previous term.
12 14
Add 4 to the previous term.
24 28
30 35
Add 5 to the previous term.
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1, 3, 5, 7, 9, ___, ____
Find the next 2 terms.
3, 5, 7, 9, 11, ___, ____
1, 4, 9, 16, 25, ___, ____
Add 2 to the previous term.
Add 3, 5, 7, 9, ...
11 13
36 49
13 15
Add 2 to the previous term.
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1, .5, .33, .25, ____, ____
Find the next 2 terms.
1, 8, 27, 64, ____, ____
10, 5, 2.5, 1.25, ____, ____
.2 .166
.625 .3125
125 216
Perfect cubes of the counting numbers
Half the previous term
1 1 1 1, , , ,...1 2 3 4
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10, 21, 32, 43, ____, ____
Find the next 2 terms.
16, 25, 36, 49, ____, ____
15, 19, 23, 27, ____, ____
54 65
31 35
64 81
Add 11 to the previous term.
Add 4 to the previous term.
Add 9, 11, 13, 15, 17 …
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9, 16, 21, 24, ____, ____
Find the next 2 terms.
16, 17, 19, 22, ____, ____
3, 32, 321, 3213, ____, ____
25 24
32132 321321
26 31
Add 7, 5, 3, 1, -1, -3 …
3, 32, 321, and repeat as add on.
Add 1, add 2, add 3, …
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Weird Sequences
A, C, E, G, ___
1, 2, 3, 5, 8, 13, ___
O, T, T, F, F, S, S, E, ___
I
N
21
Skip every other letter
First letter of each counting number
Fibbonacci Sequence: Add the previous 2 terms.
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Weird Sequences 0, .5, .67, .75, .8, ____
1, 1.141, 1.73, 2, 8, 2.24, ___
4, 6, 8, 9, 10, 12, 14, ___
.833
11 13
16
Add 2, then 2, then 1, then 1, then 2, then 2, …
0 1 2 3, , , ,...1 2 3 4
1, 2 , 3 , 4 , 5 ,...
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Weird Sequences
1, 2, 5, 20, 50, 100, ____
A, E, F, H, I, K, L, M, ___
A, K, Q, J, ___
200
10
N
Numbers on dollar bills.
Letters that are not curved.
Add 2 to the previous term.
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Weird Sequences
8, 5, 4, 9, 1, 7, 6, ____
B, C, D, G, J, ___
60, 90, 108, 120, ___
3
O
128.6
digits in alphabetical order
Curved letters
Interior angles of regular polygons
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SummarySometimes the gaps between terms are constant.
Sometimes the gaps between terms increase at a pattern.
Sometimes the next term is a multiple of the previous term. If so, this can be seen by dividing a term by the previous term.
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SummaryThe purpose of these exercises is to get practice at recognizing patterns.
Sometimes the patterns are bizzare.
It is not necessary to be able to find all the patter.
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C’est fini.Good day and good luck.
A Senior Citizen Production
That’s all folks.
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C’est fini.
Good day and good luck.