Look at the difference
What comes next in 4, 7, 10, 13? Each number is three more than the last, so the pattern suggests 16.
Writing +3, +3, +3 underneath the sequence makes the rule easy to see. Subtraction is often a useful first step, even when the numbers look less familiar.
Check changing gaps and multiplication
In 2, 5, 10, 17, the gaps are +3, +5 and +7. Continue with +9 and the next number is 26.
Now look at 3, 6, 12, 24. You could study the growing gaps, but there is a simpler description: each number doubles. That gives 48 next.
Check the rule against the whole sequence before settling on it.
Read every other number
For 2, 10, 4, 20, 6, 30, try splitting the sequence into two rows:
- First, third and fifth terms: 2, 4, 6.
- Second, fourth and sixth terms: 10, 20, 30.
One row increases by two, the other by ten. Continuing those patterns gives 8 as the next term.
Continue 5, 9, 15, 23, using gaps that increase by two.
33. The gaps are 4, 6 and 8, so the next gap is 10: 23 + 10 = 33.
Could another answer work?
A short list of numbers can fit more than one rule. Unless the question specifies the pattern, the next number is not always mathematically unique.
In a puzzle, look for a simple rule that fits every term and the answer choices. Try a constant difference, multiplication, changing gaps or alternate terms. If your explanation needs a new exception at each step, it is worth trying another approach.