Whilst I was doing the investigation of finding which numbers between 1 and 30
could be made by adding consecutive numbers together, I found out a few
things. The first thing that I realised is that when you want to try and find a
consecutive-number sum for an odd number, you can minus one from the
number, divide it by two, and then add that number to the one above that
number. For example: If you want to find at least one consecutive sum for 201,
you minus one from it - 200, then halve it - 100, then add that number and the
one above it together - 100+101 = 201. For 563, exactly the same thing:
minus one from it - 562, then halve it - 284, and then add that number and the
number above it together - 281+282= 563. It works every time. The next thing
that I found out was that the powers of two cannot be made. 2, no, 4, no, 8, no,
16, no, 32, no etc. There was a third thing that I realised... (except 1 because we
weren't allowed to use zero), the odd numbers starting from 3 are 3=1+2, 5=2+3,
7=3+4, 9=4+5 etc. There are a few more things which peole mentioned, but I
haven't discovered them yet.
I do not think that I can prove the first fact is always true, but I have tried
this sum with many numbers, and it has worked each time!! The next
thing I found out was about the fact that you can never make the powers
of two, and unfortunately, I cannot make a reason for this always being
true either. The last fact was about the sum of the odd numbers (apart
from 1) always carrying on from the second digit of the last odd number. I
can prove that this is always true with quite a long formula. n= ((n-1)/2) +
((n-1)/2) +1.
Ottilie Nye 8VL
You could still work out the numbers from
1-30, but multiply the consecutive numbers,
and see what patterns come up. You could
also only add consecutive even numbers,
or only consecutive odd numbers. These
things could all have something in
common, or there could be a pattern
between, or nothing at all, maybe? Another
thing I could try is, instead of just racing
though the numbers from 1-30, I could try
and make a formula for each of the
numbers and their sums. There are so
many different things that you can do which
aren't adding consecutive numbes to get a
number, and these are just a few of them.