Hint
What must the middle temperature be? Remember that the temperature are in degrees Celsius.
Answer
The temperatures were -6, -2, 2, 6, 10 °C.
Each day increased by a steady 4 degrees.
Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).
Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).
If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.
If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does matches all of the requirements.
If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.
Any larger increase makes the product even larger, so we can stop checking.
We then repeat this for 100, 200, 300, up to 900 – which is 200 9's.
But from 900 to 999 we have an extra 100 9's as each starts with a 9.
So the total is 300.
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