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Investigation: adding consecutive numbers
By Alan Mcilwain (P3178) on Sunday, October 29, 2000 - 09:06 am:

Hi

I am stuck on some school work and my Dad doesn't know how to help me this time. What I need to know is....

For Number patterns like:

1+2+3+4+5=15
2+3+4+5+6=20

I need to know what the

  • a) pattern is (no's go up in 5s)
  • b) prediction is (?)
  • c) Nth term (5N+10) and
  • d) why (?).
Please can you tell me what is meant by 'prediction' and 'why'

thank you very much - Alan
By Sean Hartnoll (Sah40) on Sunday, October 29, 2000 - 12:33 pm:

Hi Alan,

I think that by 'prediction' they want you to work out what the result will be in the Nth case, and the answer here is what is given in number c), that is 5N+10. So for example in the first case (N=1), the sum is 5x1+10=15 and in the second case (N=2), we see that the sum is 5x2+10=20. So we would then predict that the next case, (N=3) which is the sum 3+4+5+6+7 would be equal to 5x3+10=25, and if you do the sum you will find that it is. Basically it's not a very well worded question, the prediction is the same as the Nth term, so parts (b) and (c) are the same (because the Nth term allows you to predict).

[In an investigation like this, what is expected for "prediction" is that you will predict what will happen in a particular example you haven't tried yet. So you might say, "I think that when the first number is 100 the total will be 510", and then check by doing the adding up. It is quite a useful thing to do if you are struggling to write a formula using algebra. - The Editor]

Now 'why' means that you are meant to find out why the Nth term is what it is. This involves explaining why each sum gives 5 more than the previous one. I will give you a clue, what is the difference between one sum and the next? 4 of the 5 terms are the same, the only one that changes is the last one. So the amount it will increase by is the difference between the new term and the one that you have removed. Can you see what the difference is?

Hope this helps, write again if there are any problems,

Sean