hhehwhqhhqhhWe found out that powers of 2 (2, 4, 8, 16...) can never be made by adding together consecutive numbers together.
Answers
Answer:
We can't write every number as a sum of consecutive numbers - for example, 2, 4 and 8 can't be written as sums of consecutive numbers. In the above, 9 and 15 were the only numbers that I could find that could be written in more than one way.
If you add two consecutive numbers together, the sum is an odd number, e.g.
1+2=3
2+3=5
3+4=7
4+5=9
5+6=11
6+7=13
and so on
Explanation:
2
3 = 1+2
4
5 = 2+3
6 = 1+2+3
7 = 3+4
8
9 = 4+5 = 2+3+4
10 = 1+2+3+4
11 = 5+6
12 = 3+4+5
13 = 6+7
14 = 2+3+4+5
15 = 7+8 = 4+5+6 = 1+2+3+4+5
We can't write every number as a sum of consecutive numbers - for example, 2, 4 and 8 can't be written as sums of consecutive numbers. In the above, 9 and 15 were the only numbers that I could find that could be written in more than one way.
Many people spotted the pattern that all odd numbers (except 1) could be written as the sum of two consecutive numbers. For example, Matilda and Tamaris wrote:
If you add two consecutive numbers together, the sum is an odd number, e.g.
1+2=3
2+3=5
3+4=7
4+5=9
5+6=11
6+7=13
and so on...
Well done to pupils from Kenmont Primary School who noticed this, and explained that an Odd plus an Even is always Odd.
Some spotted a similar pattern for multiples of 3
If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.
1+2+3=6
2+3+4=9
3+4+5=12
4+5+6=15
5+6+7=18
Continuing with the patterns, the Lumen Christi grade 5/6 maths extension program team sent us:
We discovered that the sum of four consecutive numbers gave us the number sequence 10, 14, 18, 22, 26, 30, and so on. They were all even numbers that had an odd number as half of its total.
1+2+3+4=10
2+3+4+5=14
3+4+5+6=18...