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# Number Patterns-Investigation

Module by: raj singh. E-mail the author

Summary: i)An investigation involving filling in tables by applying given rules or by discovering the rule first. ii)Completing conjecture statements based on natural numbers and then proving them.

Mathematics

A. Apply the given rule to complete the tables below:

1.

 n 1 2 3 4 5 6 7 8 n-5 -4 -3

2.

 n 1 2 3 4 5 6 7 8 2n+1 3 -5

3.

 n 1 2 3 4 5 6 7 8 3n-2 1 4

4.

 n 1 2 3 4 5 6 7 8 5n+7 12 17

B. Find the rule used in each table and use it to generate the answers in each table below:

1.

 1 2 3 4 5 6 9 n 17 20 3 9 15 21 27 33

2.

 1 2 3 4 5 6 n 20 11 23 35 47 59 71

3.

 1 2 3 4 5 6 n 20 -4 4 12 20 28 36

4.

 1 2 3 4 5 6 n 20 0 7 14 21 28 35

C. Complete and then prove each of the following conjectures:

1. The sum of any two consecutive odd natural numbers is ________________
1. The sum of the any two consecutive even natural numbers is ________________

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