The only sequences from 1-7 that will contain 1000 are A-2 and A-3.
I found this by subtracting the first number from the sequence from 1000.
Then I needed to figure out whether this new number was divisible by the difference between the first and the second numbers in the sequence. If the number is divisble, then 1000 will appear in the sequence.
For example, using the first sequence:
1000- 1 = 999.
Is 999 divisible by (3-1) ?
No, it isn't, so I know that the number 1000 will never appear in the first sequence.
How did I figure this out? I knew that this problem had to do with divisibility as well as the "counting distance".
So, for example, with the first sequence, I knew that any number divisible by 2 plus the starting number would appear in the sequence.
In other words, any number divisible by the counting distance plus the starting number would be in the sequence.
To add numbers in the sequence, you just add the difference between the first two numbers.