Sequence Puzzle - First Question of 42

Professor Tera was walking on Connecticut Road, where there are some public restrooms.
Tera saw some students standing in a row. They seemed to be playing a game called Evolution.
And it looked like more and more students were joining them.
Then Tera heard a conversation between two other teachers.

One of the teachers pointed to the row of students and said:
　　"Look! He’s the worst student in my class!"
The other teacher said:
　　"Why?"
　　"We had twenty-four math tests, and he failed all of them!"
　　"How?"
　　"He got zeroes in the first two tests. And, in the third test,
　　　　he got only three points!"
　　"What about the fourth test?"
　　"Only six points. And he got twelve in the fifth test."
　　"Looks like he’s getting better and better. I suspect he’d get
　　　　twenty-four in the next one…"
　　"No, zero!" The teacher was angry.
　　"Oh, no…"
　　"He had a cold before the sixth test and was sent to hospital.
　　　　So he missed the sixth test."
　　"What about the seventh test?"
　　"Twenty-four. And then, forty, then twenty-four."
　　"Ah, forty – That’s only fifteen points below the pass mark,
　　　　but his scores seem to be dropping. What about the tenth time?"
　　"Let me think… Ah, it slipped my mind."
The conversation continued.
　　"Looks like he never met my expectation…"
　　"I agree."
　　"Yeah, you know, I promised to give him a toy spaceship once he
　　　　got a hundred."

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Find the missing terms in the sequence.

0 0 3 6 12 0 24 40 24 [___] 6 12 6 0 0 24 16 0 0 8 6 16 0 0 …

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Question 1: Find the missing terms in the sequence above.

And fill in the blanks in the extended version given in the hints!

Question 2: Try extending the sequence.

Will the student pass the next test? Will the student be sent to hospital another time?

Hint 1:

Hint 2:

Hint 3:

Hint 4:

Hint 5:

Hint 6: (Related Tags)

Hint 7: (to make Hint 5 clearer)