What is the difference between two successive sums in each box? Is it the same throughout?
For 2 consecutive numbers: Difference = 2 Sums: 3, 5, 7, 9
For 3 consecutive numbers: Difference = 3 Sums: 6, 9, 12, 15
For 4 consecutive numbers: Difference = 4 Sums: 10, 14, 18, 22
Answer: Yes, the difference is the same throughout each box. ∴ The difference equals the count of consecutive numbers being added.
Explanation
The chapter demonstrates that when we add consecutive numbers, each successive sum increases by the count of numbers being added. This is because moving to the next set means each number increases by 1, and there are n numbers, so total increase is n.
Solution Steps
For 2 consecutive numbers, the sums are 3, 5, 7, 9 with difference = 2
For 3 consecutive numbers, the sums are 6, 9, 12, 15 with difference = 3
For 4 consecutive numbers, the sums are 10, 14, 18, 22 with difference = 4
The difference between successive sums equals the count of consecutive numbers being added