"Running the Category" on the Jeopardy! TV Show

On the TV program Jeopardy! under each category, there are five different problems. They pay:

$200
$400
$600
$800
$1000

Sometimes, a contestant knows a lot about a particular subject and answers every question in a category.
Alex Trebec calls this "running the category." Without adding the five numbers, what does the contestant win for "running the category?"

Hint: the average prize is $600; there are two smaller prizes and two larger prizes. Multiply $600 by 5 to get the answer, then add up the numbers to confirm.

In "double Jeopardy" there are also five prizes. They pay:

$400
$800
$1200
$1600
$2000

Without adding the five numbers, what does the contestant win for "running the category" in Double Jeopardy? Use the same method to get the answer; it should be twice the previous answer.

The prizes form an arithmetic sequence. You can use the same idea to add up any arithmetic sequence.