This quiz helps you find the next number in the sequence and spot the rule behind each pattern. Solve quick puzzles that build your logic, from simple steps to mixed changes, with instant feedback as you go. For more practice, try our number sequence test or take a find the number quiz.
What is the next number in the sequence: 2, 4, 6, 8, ?
10
8
9
12
This is an arithmetic progression where each term increases by 2. Starting from 2, we add 2 repeatedly to get 4, 6, 8, and then 10. Recognizing constant differences is key to solving such sequences. For more on arithmetic progressions see .
Find the next number: 5, 10, 15, 20, ?
26
30
24
25
This is another arithmetic sequence with a common difference of 5. After 20, adding 5 gives 25. Identifying the constant increment quickly leads to the next term. Learn more about arithmetic series at .
What comes next: 1, 1, 2, 3, 5, ?
9
6
7
8
This is the Fibonacci sequence, where each term is the sum of the two preceding terms. After 3 and 5, the next term is 3+5=8. Fibonacci numbers appear in many natural phenomena. More details are available at .
Determine the next number: 3, 6, 9, 12, ?
14
13
18
15
This sequence increases by 3 each time, so it's an arithmetic progression with difference 3. Adding 3 to 12 yields 15. Spotting the consistent addition helps solve it. See for reference.
What is the next term in: 10, 9, 8, 7, ?
5
8
7
6
This is a decreasing arithmetic sequence with a common difference of -1. Subtracting 1 from 7 gives 6. Recognizing negative increments is as straightforward as positive ones. More at .
Find the next number: 2, 4, 8, 16, ?
64
32
30
24
This is a geometric sequence with a ratio of 2, so each term is twice the previous one. Doubling 16 gives 32. Geometric progressions grow (or shrink) by constant factors. Learn more at .
What comes next: 0, 1, 1, 2, 3, ?
7
5
6
4
This is the Fibonacci sequence starting from 0 and 1. Each term is the sum of the two preceding terms, so 2+3=5. The Fibonacci pattern appears in many contexts. See for more.
Determine the next number: 1, 3, 5, 7, ?
11
8
9
10
This sequence consists of odd numbers starting at 1, increasing by 2 each time. After 7, the next odd number is 9. Recognizing standard numeric patterns simplifies these questions. More examples at .
What is the next prime in the sequence: 2, 3, 5, 7, 11, ?
12
14
17
13
This sequence lists consecutive prime numbers. After 11, the next prime is 13. Prime numbers have no divisors other than 1 and themselves. More on primes at .
Find the next term: 1, 4, 9, 16, ?
30
20
25
27
These are perfect squares: 1², 2², 3², 4², so the next is 5²=25. Square numbers form a basic sequence in number patterns. For details see .
Determine the next number: 1, 3, 6, 10, 15, ?
20
22
21
18
This is the sequence of triangular numbers: each term adds an increasing integer (2, 3, 4, 5...). After 15, adding 6 gives 21. Triangular figures are common in combinatorics. More at .
What comes next: 1, 2, 6, 24, ?
720
48
36
120
This sequence lists factorials: 1! = 1, 2! = 2, 3! = 6, 4! = 24, so 5! = 120. Factorials grow very quickly and appear in permutations/combinations. See .
Find the next term: 3, 5, 8, 12, 17, ?
25
24
22
23
The differences here increase by 1 each time: +2, +3, +4, +5. Adding 6 to 17 yields 23. Recognizing how increments change is key. More patterns at .
What is the next number: 1, 2, 4, 7, 11, ?
14
17
16
15
Each term increases by 1 more than the previous increment: +1, +2, +3, +4, so next is +5. Thus 11 + 5 = 16. Increasing step sizes are a common pattern. Details at .
Find the next number: 2, 4, 12, 48, ?
192
240
360
200
Here each term is multiplied by an increasing integer: ×2, ×3, ×4, so next is 48 × 5 = 240. Recognizing changing multipliers reveals the pattern. Learn more at .
What comes next: 1, 3, 4, 7, 11, 18, ?
29
28
31
30
This is a Fibonacci-like sequence where each term is the sum of the two preceding terms. 11 + 18 = 29 gives the next value. Variations of Fibonacci often start with different seeds. See .
Determine the next number: 3, 4, 7, 12, 19, 28, ?
39
40
36
37
The differences form the odd numbers 1, 3, 5, 7, 9, so the next difference is 11. Adding 11 to 28 yields 39. Recognizing this secondary pattern is key. More at .
What is the next term: 1, 4, 27, 256, 3125, ?
4096
46656
16807
7776
Each term follows n^n: 1^1, 2^2, 3^3, 4^4, 5^5, so next is 6^6 = 46656. Self-powers grow extremely quickly. Read more on self-powers at .
Find the next number: 2, 4, 16, 256, ?
1024
65536
4096
16384
Each term is the previous term squared: 2²=4, 4²=16, 16²=256, so 256²=65536. Recognizing exponentiation in sequences is crucial. See exponentiation details at .
Determine the next term: 1, 1, 2, 6, 24, 120, ?
360
504
144
720
This is the sequence of factorials: n! for n starting at 0 or 1. After 5! = 120 comes 6! = 720. Factorials appear in permutations and combinations. More at .
What comes next: 5, 11, 23, 47, 95, ?
190
193
189
191
Each term is obtained by doubling the previous term and adding 1 (n ? 2n + 1). After 95, 2×95 + 1 = 191. Linear recurrences like this are common in challenging sequences. See more at .
Find the next number: 7, 10, 8, 11, 9, 12, ?
13
11
10
14
This alternates between adding 3 and subtracting 2. 7+3=10, 10?2=8, 8+3=11, etc. After 12, we subtract 2 to get 10. Alternating patterns require tracking two operations. Read more at .
Determine the next term: 1, 2, 8, 48, 384, ?
1920
3840
2304
3072
Each term is multiplied by an even number that increases by 2: ×2, ×4, ×6, ×8, so next is 384 × 10 = 3840. This uses a changing multiplier sequence. See examples at .
What is the next element of the look-and-say sequence: 1, 11, 21, 1211, 111221, ?
212211
312211
13112221
11131221
This is the classic look-and-say sequence, where you describe the previous term's digits. '111221' is read as 'three 1s, two 2s, one 1' giving '312211'. See details at .
Find the next number: 1, 2, 5, 12, 29, 70, ?
169
140
119
210
This sequence follows the Pell recurrence: P_n = 2·P_{n?1} + P_{n?2} with P_0=1, P_1=2, etc. After 70 and 29, 2×70 + 29 = 169. Pell numbers grow like continued fraction convergents of ?2. More on Pell numbers at .
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Study Outcomes
Analyze Number Sequences -
Learn to dissect various sequence puzzles by identifying differences, ratios, and other mathematical relationships.
Apply Pattern Recognition -
Develop the ability to spot recurring themes and structures within the free pattern quiz.
Predict Next Terms -
Use logical reasoning and mathematical rules to determine the next number in a sequence.
Differentiate Sequence Types -
Understand distinct sequence puzzles - arithmetic, geometric, and more complex number patterns.
Enhance Analytical Skills -
Improve problem-solving speed and accuracy through engaging practice with number sequence quizzes.
Cheat Sheet
Arithmetic Progressions -
Arithmetic sequences follow the formula aₙ = a + (n - 1)d, where d is the common difference. Spot this in a pattern quiz by checking if successive terms increase or decrease by the same amount. For example, in 3, 7, 11, 15,… the constant difference d=4 makes predicting the next term immediate (19).
Geometric Sequences -
In a number sequence quiz, geometric patterns multiply by a constant ratio r: aₙ = a·r❿❻¹. Test for this by dividing consecutive terms - if the ratio stays constant (e.g., 2, 6, 18, 54… has r=3), you've found the rule. Many math pattern quizzes feature this type, so remembering "divide to verify" is a handy mnemonic.
Second Differences & Quadratic Patterns -
When first differences aren't constant, compute second differences: a constant value indicates a quadratic rule of form an² + bn + c. According to MIT OpenCourseWare, this helps decode puzzles like 2, 6, 12, 20… where second differences are all 2, implying n² + n. Use simple tables to track differences side by side.
Fibonacci & Recurrence Relations -
The famous Fibonacci sequence (1, 1, 2, 3, 5, 8…) follows Fₙ = Fₙ₋ + Fₙ₋₂, a core example in sequence puzzles researched by the OEIS. Look for patterns where each term sums the two preceding ones - this trick surfaces often in advanced pattern quizzes. A quick memory phrase: "last two make the next," keeps your focus sharp.
Prime & Special Number Patterns -
Some sequence puzzles hinge on prime numbers (2, 3, 5, 7, 11…) or other sets like triangular or square numbers. The Prime Pages and Wolfram MathWorld provide extensive lists to verify candidates. If differences or ratios fail, consider testing primality or known figurate forms to crack these tricky number patterns.
