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Four numbers are in arithmetic progression with a mean of 24 and a common difference of 4. What is the product of the first and last numbers?
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Solution: Step 1: Let the four numbers be x, x+d, x+2d, and x+3d where d = 4. Step 2: The mean of the four numbers is (x + x+d + x+2d + x+3d)/4 = 24. Step 3: This simplifies to (4x + 6d)/4 = 24. Step 4: Substituting d = 4, we get (4x + 24)/4 = 24. Step 5: Solving for x, 4x + 24 = 96. Step 6: Therefore, 4x = 72 and x = 18. Step 7: The first and last numbers are 18 and 18+3*4 = 30. Step 8: The product of the first and last numbers is 18 * 30 = 540.
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