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Consecutive Numbers An Investigation

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**This investigation explores the answers you get when **

Consecutive Numbers This investigation explores the answers you get when you add consecutive numbers together Consider the following examples: 1 + 2 = 3 ; = 5 ; = 7 ; = etc. These examples show the sum of two consecutive numbers. Write down some of the sums of three consecutive numbers. One is done for you. Write down some more. = 6. Question: Can the number 36 be written as the sum of two, three, four or five consecutive numbers? To answer this question the table on the next slide is formed.

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**Put some more numbers into their correct columns. **

Sum of 2 Consecutive numbers Sum of 3 consecutive Sum of 4 Sum of 5 3 6 10 15 5 9 14 20 7 12 28 25 32 30 Put some more numbers into their correct columns. Can you see how to make a quick test to see whether 36 is the sum of two, three, four or five consecutive numbers.

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**Choose any number of your own less that 50. **

Check whether it is the sum of two, three, four or five consecutive numbers. Extend the table to include sums of six and seven consecutive numbers. Now explore all the numbers less than 50 that cannot be written as sums of consecutive numbers.

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