1SimpleNWierdSequences

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Inductive Reasoning

1 2 3 4 5 6 … n … 20

0 3 10 21 36 55 … ? … ?

Sequences

Terms: 4, 5, 6, 7, 8 …

Terms: A, C, E, G, …

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.

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.

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

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 …

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, …

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.

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 ,...

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.

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

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.

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.

C’est fini.Good day and good luck.

A Senior Citizen Production

That’s all folks.

C’est fini.

Good day and good luck.