In each of the boxes above, state whether the sums are even or odd. Explain why this is happening.
Sum of 2 consecutive numbers: Always odd Reason: one even + one odd = odd
Sum of 3 consecutive numbers: Alternates between even and odd Reason: sum = 3 × middle number, so depends on middle number
Sum of 4 consecutive numbers: Always even Reason: two evens + two odds = even
Explanation
The chapter shows patterns in consecutive number sums. For 2 consecutive numbers: one even + one odd = odd. For 3 consecutive numbers: the sum equals 3 times the middle number. For 4 consecutive numbers: two evens + two odds = even.
Solution Steps
Sum of 2 consecutive numbers: Always odd (one even + one odd = odd)
Sum of 3 consecutive numbers: Alternates between even and odd (sum = 3 × middle number, so depends on middle number)
Sum of 4 consecutive numbers: Always even (two evens + two odds = even)