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# Consecutive Sums

Extracts from this document...

Introduction

Consecutive Sums Someone tells you that it is possible to make any number by writing an addition sum using only consecutive numbers. EXAMPLE 18 = 3 + 4 + 5 + 6 6 = 1 + 2 + 3 21 = 1 + 2 + 3 + 4 + 5 + 6 A) Is this person right? B) Can you make every number? C) Investigate and write down everything that you notice, as you go along. (E.g. patterns) ____________________________________________ A) This person must be wrong as they said you could make "any number" and I cannot make 8,16,32,40,56,64,80,88,96 this is not any number I feel this is sufficient proof to say that you can not make 'any' number. ...read more.

Middle

The more consecutive numbers the bigger the gap between each sum. E.g. 2 Consecutive Numbers I noticed that all of these consecutive numbers are all odd numbers 3,5,7,9,11.I also noticed that an Nth term could be found. E.g. 1 2 3 4 5 3 5 7 9 11 2 2 2 2 Nth term = 2n 100th term = 2 x 100 + 1= 201 I want the 3rd term I know that the term will be 7 but I need to make sure my theory works. E.g. 1 2 3 4 5 3 5 7 9 11 2 2 2 2 Nth term = 2n 3rd term = 2 x 3 + 1=7 3 Consecutive Numbers I am going to try and find out the nth term for 3 consecutive numbers. ...read more.

Conclusion

Nth term = 4n 3rd term =4 x 3 + 2 = 14 I have now proved that theory is correct I can find any term which 4 consecutive numbers make. 5 Consecutive Numbers Now I am going to find out the Nth term for 5 consecutive numbers. 1 2 3 4 5 11 15 20 25 30 5 5 5 5 Nth term = 5n 100th term = 5 x 100 + 5 = 505 Now I will have to make sure it works. Nth term = 5n 3rd term = 5 x 3 + 5 = 20 The theory is right I can now find any term, which is made by 5 consecutive numbers. ...read more.

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