Three ways to untangle
a number sequence.

Start with the simplest relationship you can test. A short sequence can fit many invented formulas; the useful rule is the one consistently supported by the exercise.

1. Inspect the differences

In 5, 9, 15, 23, ?, the gaps are 4, 6, and 8. If those gaps continue increasing by 2, the next gap is 10 and the next term is 33. Looking at the gaps transforms a less obvious sequence into a simpler one.

A constant ratio suggests multiplication instead. For 3, 9, 27, ?, dividing each term by the one before it gives 3. That points to 81.

2. Check for alternating operations

Consider 5, 15, 13, 39, 37, ?. One operation does not describe all the neighboring terms. Alternating ×3 and −2 does: 5×3=15, 15−2=13, 13×3=39, 39−2=37, then 37×3=111.

Write the operations between the numbers. Seeing “×3, −2, ×3, −2” is easier than holding all the transitions in memory.

3. Split odd and even positions

In 1, 12, 3, 10, 5, 8, ?, the odd-positioned terms are 1, 3, 5; the even-positioned terms are 12, 10, 8. One subsequence increases by 2 while the other decreases by 2. The missing odd-positioned term is 7.

Check the whole rule

Once you find a candidate answer, run the rule through all the given terms. Avoid changing the rule halfway through merely to reach a preferred option. Finite sequences are not mathematically unique without additional constraints, so a good practice question should offer enough structure and clear options to make its intended rule reasonable.

Familiarity with number-question formats is a practice skill. This guide does not measure general intelligence or promise that practice will increase IQ.