What you are actually practicing
1, 2, 1, 3, 1, 4 looks like noise until you read it by position instead of in order. The first, third and fifth terms are all 1; the second, fourth and sixth climb by one. It is two sequences printed as one.
Splitting a single stream into two channels is the whole skill, and it is the same move used in reading tables and in following two variables at once.
How the game works
You are shown six or eight terms and four candidates. Pick the next term. A wrong pick reveals it immediately.
Easy uses a constant value alternating with a short climb. Medium makes the climb steeper. Hard uses eight terms, so the pattern has more room to hide.
The relationships worth knowing
Constant alternating with rising: 1, 2, 1, 3, 1, 4 → 1.
Two rising patterns: 2, 5, 4, 8, 6, 11 → 8 — odd places climb by 2, even by 3.
The answer is often the constant, because the next position falls on the repeating channel.
Strategies that actually raise your score
Count positions first. Say "first, third, fifth" and read only those. If they repeat, the answer is that value and you can stop.
Decide which channel the missing term belongs to. With six terms shown, the seventh is an odd position — the same channel as the first term. Getting this one step right decides everything.
Do not subtract across the gap. 2 − 1 = 1 then 1 − 2 = −1 looks like nonsense, which is the clue that you are reading one sequence instead of two.
Use the visible repeat as a shortcut. If the same number appears three times at regular intervals, the answer is almost certainly that number — check the other channel only if it is not among the options.