Sum of four consecutive even numbers is 60. Find the product of second and…

Concept: Four consecutive even numbers differ by 2 each, so they can be written as x, x+2, x+4, x+6. Their sum reduces to a single linear equation in x, and solving that one equation fixes the entire sequence.

Working:

1. Let the four consecutive even numbers be x, x+2, x+4, x+6.

2. Sum = x + (x+2) + (x+4) + (x+6) = 4x + 12.

3. Set 4x + 12 = 60, so 4x = 48, giving x = 12.

4. The four numbers are 12, 14, 16, 18.

5. Second number = 14, third number = 16, so their product = 14 × 16 = 224.

Check: 12 + 14 + 16 + 18 = 60, which matches the given sum, confirming the sequence is correct.

Answer: The product of the second and third numbers is 224.