What Number Comes Next: 2, 6, 12, 20, 30? Answer Explained
What number comes next in 2, 6, 12, 20, 30? The answer is 42. The gaps between the numbers are 4, 6, 8 and 10, growing by 2 each time, so the next gap is 12 and 30 + 12 = 42. You can also see each term as a number times the next one up: 1×2, 2×3, 3×4, 4×5, 5×6, and then 6×7 = 42.
If "what comes next" puzzles make you freeze, or you guess before you've found the rule, IQ Tester pinpoints which one it is and trains it. Find my weak spots
The answer: 42
Here's the sequence laid out with both methods side by side:
| Position (n) | Term | Gap from previous | n × (n + 1) |
|---|---|---|---|
| 1 | 2 | 1 × 2 | |
| 2 | 6 | +4 | 2 × 3 |
| 3 | 12 | +6 | 3 × 4 |
| 4 | 20 | +8 | 4 × 5 |
| 5 | 30 | +10 | 5 × 6 |
| 6 | 42 | +12 | 6 × 7 |
| 7 | 56 | +14 | 7 × 8 |
So the full series runs 2, 6, 12, 20, 30, 42, 56, 72 and on. The 2 6 12 20 and 30 42 next number after that is 56.
Method 1: the gaps grow by 2
This is the route most people find first, and it's the standard move for any number sequence.
- Write the gaps: 6 − 2 = 4, 12 − 6 = 6, 20 − 12 = 8, 30 − 20 = 10.
- Look at the gaps: 4, 6, 8, 10. They go up by 2 each time.
- Extend the gaps: the next one is 12.
- Add it: 30 + 12 = 42.
That's called a second-level pattern. The numbers themselves don't have a constant step, but their gaps do. Writing a "gaps of the gaps" row is one of the most useful habits for any what comes next in the sequence puzzle.
Why people get it wrong
The quick wrong answers are usually 40 (adding 10 again) and 50 (thinking the tens pattern continues). Both come from spotting part of the pattern and stopping. Checking the gaps all the way through prevents that.
Method 2: n times (n+1)
Now look at each term on its own, not the gaps:
- 2 = 1 × 2
- 6 = 2 × 3
- 12 = 3 × 4
- 20 = 4 × 5
- 30 = 5 × 6
Every term is a whole number multiplied by the next whole number. So the 6th term is 6 × 7 = 42.
That gives you the 2 6 12 20 30 formula: term n = n × (n + 1), which you can also write as n² + n.
A name for these numbers
Numbers you get by multiplying two back-to-back whole numbers are sometimes called pronic or oblong numbers. "Oblong" makes sense if you picture them: 2 dots in a 1×2 rectangle, 6 dots in a 2×3 rectangle, 12 in a 3×4, and so on. Each one is a rectangle just one row longer than it is wide.
A neat connection
Each pronic number is exactly double a triangular number. Triangular numbers run 1, 3, 6, 10, 15, 21. Double them: 2, 6, 12, 20, 30, 42. Same sequence.
Why two methods help
You might wonder why bother with a second route when the first one works.
- It's a built-in check. If both methods give 42, you can be sure. On a timed test, that confidence saves you from second-guessing.
- Some sequences only crack one way. Gap tables work well for slow-growing series. Multiplying or factoring works better for fast-growing ones. Knowing both widens what you can solve.
- It trains flexible thinking. Getting stuck on one approach is a big reason people freeze. Having a Plan B keeps you moving.
A good habit: when you solve any sequence, ask "is there another way to see this?" Even if you don't find one, the question trains you to look. We cover the same double-route trick for the 3, 5, 9, 17 sequence, where "doubling gaps" and "double minus one" both lead to 33.
This is where practicing alone gets fuzzy. You got the answer, but did you get it through the rule, or by a lucky guess? And would you spot the same move tomorrow? IQ Tester's 16 questions show whether pattern spotting, mental arithmetic or rushing then freezing is your real sticking point, then give you one 10-minute drill a day for it, with a history so you can see if you're getting quicker. Find my weak spots
Five sequences like it
Try each one before reading the answer. Write the gaps first, then look for a multiplication.
1. What number comes next: 1, 4, 9, 16, 25?
36. These are square numbers: 1², 2², 3², 4², 5², then 6². The gaps (3, 5, 7, 9) grow by 2, just like our main puzzle, but they start at 3 instead of 4.
2. What number comes next: 2, 4, 8, 16?
32. Each number doubles. The gaps (2, 4, 8) double too.
3. What number comes next: 1, 3, 6, 10, 15?
21. Triangular numbers. Gaps are 2, 3, 4, 5, then 6. Double each one and you get our original 2, 6, 12, 20, 30 sequence.
4. What number comes next: 0, 2, 6, 12, 20?
30. It's the same pronic sequence shifted one place: n × (n − 1), starting at n = 1.
5. What number comes next: 3, 8, 15, 24, 35?
48. Gaps are 5, 7, 9, 11, then 13. Or: each term is one less than a square (4 − 1, 9 − 1, 16 − 1, 25 − 1, 36 − 1, then 49 − 1).
Notice how many of these share the "gaps grow by 2" shape. Once you know it, a whole family of puzzles opens up.
Practicing sequence spotting
A short routine you can do in about 10 minutes:
- Warm up with three easy sequences (constant gaps).
- Do two "gaps of the gaps" sequences like 2, 6, 12, 20, 30.
- Do one sequence two ways. Force yourself to find a second route.
- Make one of your own and give it to a friend or family member.
- Say the rule out loud every time, before saying the answer.
Mix in letters and shapes once numbers feel easy. Our 12 worked pattern recognition examples has plenty of each.
Get quicker at what comes next
Now you know what number comes next in 2, 6, 12, 20, 30, and two solid ways to prove it. IQ Tester's 16-question check takes about two minutes and tells you whether pattern spotting, mental arithmetic or something else is what slows you down on sequences. After that, you get one tip and one roughly 10-minute drill every day, weighted toward your weak spots, plus a streak to keep you going.
FAQ
What is the next number in 2, 6, 12, 20, 30?
It's 42. The gaps grow by 2 (4, 6, 8, 10), so the next gap is 12. Or multiply 6 × 7, since each term is n × (n + 1).
What is the formula for 2 6 12 20 30?
Term n = n × (n + 1), also written n² + n. For n = 6, that's 36 + 6 = 42.
What comes after 42 in the sequence 2, 6, 12, 20, 30?
56, then 72, then 90. The gaps keep growing by 2: 14, 16, 18.
What number comes next in 1, 4, 9, 16, 25?
- They're square numbers, so the next is 6 × 6. The gaps (3, 5, 7, 9) grow by 2, just like in 2, 6, 12, 20, 30.
How do you find what comes next in the sequence quickly?
Write the gaps, then the gaps between the gaps. If that fails, try multiplying or factoring each term. Say the rule out loud before answering, and check it with a second method if you can.