Next Number in the Sequence 3 5 9 17? The Answer and Rule
The next number in the sequence 3 5 9 17 is 33. The gaps between the numbers double each time (2, 4, 8, then 16), so you add 16 to 17. Another way to see it: double the last number and subtract 1, since 17 × 2 − 1 = 33.
If sequences like this take you a while and you're not sure whether it's the pattern or the arithmetic slowing you down, IQ Tester finds out in about two minutes. Find my weak spots
The answer: 33
Here's the whole series with the next few terms:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Term | 3 | 5 | 9 | 17 | 33 | 65 | 129 |
| Gap to next | +2 | +4 | +8 | +16 | +32 | +64 |
So 3, 5, 9, 17, 33, 65, 129 and onward. Every step roughly doubles the size of the number.
Spotting the doubling gap
When you see a number series and nothing jumps out, the first move is always the same: write the gaps.
- 3 to 5: +2
- 5 to 9: +4
- 9 to 17: +8
Now look at the gaps themselves: 2, 4, 8. Each is double the last. That's the 3 5 9 17 pattern. The next gap is 8 × 2 = 16, and 17 + 16 = 33.
It's easy to trip here, and it's the most common mistake on this puzzle. People find the doubling rule, then apply it to the wrong thing: doubling 17 to get 34, or doubling the wrong gap. Saying the rule out loud fixes it: "The gap doubles. Last gap was 8, so this gap is 16."
The second way to see it: double minus one
Look at each number compared with the one before:
- 3 × 2 − 1 = 5
- 5 × 2 − 1 = 9
- 9 × 2 − 1 = 17
- 17 × 2 − 1 = 33
Same answer, different route. Having two ways to reach a result is a great check. If both give 33, you can be confident.
The formula behind it
If you want a 3 5 9 17 sequence formula (sometimes called the nth term), here it is:
Term n = 2ⁿ + 1
Check it:
| n | 2ⁿ | 2ⁿ + 1 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 4 | 5 |
| 3 | 8 | 9 |
| 4 | 16 | 17 |
| 5 | 32 | 33 |
Every term is a power of 2, plus 1. That's why the gaps double: the gap between 2ⁿ + 1 and 2ⁿ⁺¹ + 1 is just 2ⁿ, which doubles each step.
What about 2 3 5 9 17?
You'll also see this version with a 2 at the front. The 2 3 5 9 17 next number is also 33. The gaps are 1, 2, 4, 8, and then 16. In formula terms, the sequence starts one step earlier: 2⁰ + 1 = 2. Same rule, one extra term.
Why it is a classic IQ item
This 3 5 9 17 series shows up in aptitude tests, school worksheets and online IQ quizzes for a few good reasons:
- The first-level gaps aren't constant. Anyone who only checks for "add the same number" gets stuck.
- It rewards a second look. You have to find a rule in the gaps, which is a pattern inside a pattern.
- It has two valid routes. Doubling gaps and double-minus-one both work, so it checks flexible thinking.
- It punishes rushing. The quick wrong answers (25, by adding 8 again; or 34, by doubling 17) are both tempting.
It's a clean test of two skills at once: pattern spotting and mental arithmetic. For more classic items with full reasoning, see hard IQ test questions with answers explained.
Three sequences like it
Try these before looking at the answers. Write the gaps first.
1. 4, 7, 13, 25, ?
2. 2, 5, 11, 23, ?
3. 1, 3, 7, 15, ?
Answers:
- 49. Gaps are 3, 6, 12, so next is 24. Or: double and subtract 1 (25 × 2 − 1 = 49).
- 47. Gaps are 3, 6, 12, then 24. Or: double and add 1 (23 × 2 + 1 = 47).
- 31. Gaps are 2, 4, 8, then 16. Or: each term is 2ⁿ − 1.
Notice that all three are the same idea as 3 5 9 17 wearing a different starting number. Once you've seen the doubling-gap family, you'll spot it on sight. A close cousin with growing by 2 gaps is 2, 6, 12, 20, 30, which is worth comparing.
Here's what's tough to judge alone: when you get one of these wrong, was it the pattern, the arithmetic, or rushing past the check? From the inside it all feels like "I got it wrong." IQ Tester's 16 questions separate pattern spotting, mental arithmetic and rushing into different weak spots, then pick your daily drill to match. Find my weak spots
The say-it-out-loud drill
This drill turns "what number comes next" puzzles from guessing into a method. It takes about three minutes.
- Write the sequence. Leave space underneath.
- Write the gaps. Say them: "plus 2, plus 4, plus 8."
- Say what the gaps are doing. "The gaps double."
- Say the next gap. "Next gap is 16."
- Say the answer and check it a second way. "33. Double 17 is 34, minus 1 is 33. Matches."
Do this with five sequences a day for a week. By the end, the steps happen in your head, and you'll catch the wrong-gap mistake before it happens.
A few more to practice on (answers at the end of the FAQ):
- 6, 7, 9, 13, 21, ?
- 10, 11, 13, 17, 25, ?
Solve the next sequence faster
You now know the next number in the sequence 3 5 9 17 is 33, and why. IQ Tester's 16-question check takes about two minutes and shows whether pattern spotting or mental arithmetic is the part that slows you down. Then you get one tip and one roughly 10-minute drill each day, like "Name the rule out loud," weighted toward your weak spots.
FAQ
What is the next number in 3 5 9 17?
It's 33. The gaps are 2, 4 and 8, doubling each time, so the next gap is 16. You can also double the last number and subtract 1: 17 × 2 − 1 = 33.
What is the 3 5 9 17 sequence formula?
The nth term is 2ⁿ + 1. For n = 1 to 5, that gives 3, 5, 9, 17 and 33.
What comes after 33 in the 3 5 9 17 series?
65, then 129, then 257. Each gap doubles again: 32, 64, 128.
What is the 2 3 5 9 17 next number?
It's also 33. The gaps are 1, 2, 4, 8, so the next gap is 16. It's the same sequence with one extra term at the start.
How do I find what number comes next in any sequence?
Write the gaps, then check if the gaps follow a rule. If not, try multiplying, then squares and cubes, then two alternating rules. Practice answers from above: 6, 7, 9, 13, 21 gives 37 (gaps 1, 2, 4, 8, 16), and 10, 11, 13, 17, 25 gives 41.