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# Consecutive Sums

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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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