Understanding the Number Sequence
When we add counting numbers up and then down, we create a unique sequence that reflects a pattern. Let's break down the process.
Counting Numbers Sequence
- The counting numbers start from 1 and increase by 1 with each step:
1, 2, 3, 4, 5, ...
Adding Up
- When we add the counting numbers up to a certain point, for example, 5, we have:
- 1 + 2 + 3 + 4 + 5 = 15
Adding Down
- Now, we reverse this sequence and add down from 5 back to 1:
- 5 + 4 + 3 + 2 + 1 = 15
Combining Both Sequences
- When we combine both sequences, we notice a pattern:
- Up: 1, 2, 3, 4, 5
- Down: 5, 4, 3, 2, 1
- The combined sequence becomes:
1, 2, 3, 4, 5, 4, 3, 2, 1
Resulting Sequence
- The resulting sequence shows that the numbers increase to the peak (5) and then decrease back down to 1.
Conclusion
- The sequence created by adding counting numbers up and then down is symmetric and reflects a peak at the maximum number. This pattern can be used to understand various mathematical concepts, such as sequences and symmetry.
By observing this simple yet elegant sequence, students can appreciate the beauty of numbers and their relationships.