Quandaries
and Queries
hi my name is yas and I am a year 9 student
i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5
this is what i am working on can u please help me i am not to sure about this all.
thank
Hi Yas,
There are lots of interesting properties about the sums of consecutive integers. Let me show you one. I am going to add 1, 2, 3, 4, 5 and 6.
One procedure is to start at 1 and go to 6.
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
Another procedure is to start at 6 and go to 1.
6 + 5 = 11
11 + 4 = 15
15 + 3 = 18
18 + 2 = 20
20 + 1 = 21
A third procedure is to start at both ends and work toward the middle
1 + 6 = 7
2 + 5 = 7
3 + 4 = 7
and finally 73 = 21
If you were asked to add 1, 2, 3, 4,..., 100, that is the consecutive integers from 1 to 100, which procedure would you rather use?
Penny