We have been quite lucky with the weather recently, it has got steadily warmer each day, over the last five days.

By this, I mean that the temperature rose by the same amount each day.

The average temperature was 2 °C and I know it froze on two occasions.

I also know the product of the temperatures was over 500 but below 2,000 and each temperature was an integer.

What were the last 5 temperatures?

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Hint

What must the middle temperature be?

Answer

The temperatures were -6, -2, 2, 6, 10 °C.

Each day increased by a steady 4 degrees.

As the temperature rose steadily each day and the average was 2 degrees, we know the middle temperature was 2 degrees.

If we assume a daily increase of 1, the sequence would be 0, 1, 2, 3, 4. This doesn't work we require 2 negative temperatures.

If we assume a daily increase of 2, the sequence would be -2, 0, 2, 4, 6. This doesn't work we require 2 negative temperatures.

If we assume a daily increase of 3, the sequence would be -4, -1, 2, 5, 8. This doesn't work as the product is less than 500.

If we assume a daily increase of 4, the sequence would be -6, -2, 2, 6, 10. This matches all of the requirements.

If we assume a daily increase of 5, the sequence would be -8, -3, 2, 7, 12. This doesn't work as the product is more than 2000.

So the only possible answer is -6, -2, 2, 6, 10.