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Quizzes > Mathematics > Algebra

Sequence & Series IQ Test: Challenge Your Number Skills

Ready for a number patterns test? Think you can ace this sequence exam?

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art numbers forming a sequence on layered sheets over dark blue background symbolizing a sequence and series IQ quiz

This Sequence & Series IQ quiz helps you solve number sequences and predict the next term. Use it to practice for IQ-style questions, sharpen your reasoning, and check for gaps before a test. When you want extra practice, try the number series set or the sequences collection .

What is the next number in the sequence? 2, 4, 6, 8, ...
10
14
9
12
This is a simple arithmetic sequence increasing by 2 each time. After 8, adding 2 gives 10. Using the general formula for an arithmetic sequence a_n = a_1 + (n-1)d confirms this. .
What comes next? 5, 10, 15, 20, ...
25
22
30
23
This is an arithmetic sequence with a common difference of 5. Adding 5 to 20 yields 25. The nth term is a_n = 5n. .
Find the next Fibonacci number: 1, 1, 2, 3, 5, ...
7
10
6
8
In the Fibonacci sequence each term is the sum of the two preceding terms: 3+5=8. The sequence starts 1, 1, 2, 3, 5, 8. .
What is the next number? 3, 6, 9, 12, ...
18
15
14
13
This sequence increases by 3 each time. After 12, adding 3 gives 15. It follows a_n = 3n for n starting at 1. .
What comes next in the geometric sequence? 2, 4, 8, 16, ...
32
24
48
64
This is a geometric sequence with ratio 2. Multiplying 16 by 2 yields 32. The general term is a_n = 2^n. .
Find the next square number: 1, 4, 9, 16, ...
25
20
30
18
These are perfect squares: 1^2, 2^2, 3^2, 4^2, so the next is 5^2 = 25. Square numbers follow n^2. .
What is the next term? 10, 9, 8, 7, ...
5
7
6
4
This sequence decreases by 1 each time. Subtracting 1 from 7 gives 6. It is an arithmetic sequence with common difference -1. .
What is the next prime number in the sequence? 2, 3, 5, 7, 11, ...
13
12
15
14
These are consecutive primes. After 11, the next prime is 13. Primes are numbers with exactly two positive divisors. .
Find the next term: 2, 6, 12, 20, 30, ...
36
48
42
40
The nth term is n(n+1): 1×2=2, 2×3=6, …, 6×7=42. This sequence of pronic numbers follows that formula. .
What is the next number? 2, 5, 10, 17, 26, ...
39
37
35
34
Each term is n^2+1: 1^2+1=2, 2^2+1=5, …, 6^2+1=37. This quadratic pattern yields the given values. Quadratic functions.
Find the next factorial term: 1, 2, 6, 24, 120, ...
840
720
600
7200
This is the factorial sequence: n! for n=1,2,3,…, 6! = 720. Factorials multiply all positive integers up to n. .
What comes next? 7, 10, 8, 11, 9, 12, ...
11
13
10
14
Odd positions start at 7 and add 1 each time (7,8,9,…), even positions start at 10 and add 1 (10,11,12,…). The 7th term is the odd-position pattern: 9+1=10. .
Determine the next term: 4, 6, 9, 6, 14, 6, ...
16
18
24
19
Even positions are constant 6. Odd positions increase by 5: 4, 9, 14, so next odd is 14+5=19. .
What is the next number? 3, 5, 9, 17, 33, ...
65
63
57
61
Differences double each time: +2, +4, +8, +16. The last term 33 + 32 = 65. This exponential difference pattern is common. .
Find the next term: 3, 8, 15, 24, 35, ...
49
48
45
40
Differences are odd numbers increasing by 2: +5, +7, +9, +11. Adding 13 to 35 gives 48. .
What is the next number? 6, 11, 21, 36, 56, ...
81
76
78
82
Differences are multiples of 5: +5, +10, +15, +20, next +25 = 81. The pattern is n×5 added each step. .
Find the next term: 1, 4, 10, 19, 31, ...
43
55
50
46
Differences grow by 3: +3, +6, +9, +12. Next difference is +15, so 31+15 = 46. This second-difference pattern is linear. .
What is the next term? 2, 4, 16, 256, ...
4096
65536
1024
16384
Each term is 2 raised to the previous term: 2^2=4, 2^4=16, 2^16=65536. Next would be 2^256, but the 4th term itself is 65536. .
Find the next term: 1, 2, 6, 42, 1806, ...
40320
720720
3263442
3628800
Each term is prior term times its index plus 1: 6×7=42, 42×43=1806, then 1806×1807=3263442. This is Sylow's factorial sequence. .
What comes next? 4, 11, 20, 31, 44, ...
57
56
59
61
Differences increase by 2: +7, +9, +11, +13. The next difference is +15, giving 44+15 = 59. This is a quadratic type progression. .
Find the next Catalan number: 1, 1, 2, 5, 14, 42, 132, ...
455
429
462
419
Catalan numbers follow C_{n+1} = ?_{i=0..n} C_i*C_{n-i}. The 8th Catalan is 429. These count certain combinatorial structures. .
What is the next term? 1, 5, 12, 22, 35, 51, ...
75
70
65
60
These are pentagonal numbers given by n(3n?1)/2 for n=1,2,3… The 7th term is 7*(20)/2 = 70. .
Find the next number: 1, 5, 14, 30, 55, ...
95
100
91
85
This sequence adds square numbers: +4, +9, +16, +25, next +36 = 91. It follows a_n = a_{n-1} + n^2. .
What is the next central binomial coefficient? 1, 2, 6, 20, 70, 252, ...
924
792
9240
780
These are C(2n,n) for n=0,1,2…; C(12,6) = 924. Central binomial coefficients appear in combinatorics. .
Find the next term: 1, 3, 15, 105, 945, ...
10945
9450
10080
10395
Multiply by consecutive odd numbers: 1×3=3, 3×5=15, …, 945×11 = 10395. This factorial-like pattern uses odd factors. .
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Study Outcomes

  1. Identify Sequence Patterns -

    Recognize common series types such as arithmetic, geometric, and Fibonacci to lay the groundwork for solving complex sequences in this numeric sequence challenge.

  2. Analyze Numeric Relationships -

    Break down number patterns test items by examining differences, ratios, and functional rules to understand how elements interconnect.

  3. Predict Next Elements -

    Apply rule-based strategies to forecast subsequent numbers with confidence, mastering techniques central to any sequence exam.

  4. Enhance Problem-Solving Speed -

    Develop time-management skills and mental shortcuts to increase accuracy and efficiency when tackling iq test numbers under pressure.

  5. Evaluate Your Performance -

    Interpret quiz results to identify strengths and areas for improvement, guiding focused practice beyond the sequence series quiz.

Cheat Sheet

  1. Arithmetic Progressions (AP) -

    In an AP, each term increases by a constant difference d following the formula aₙ = a₝ + (n−1)d, which helps you forecast future terms. Master this concept to quickly solve iq test numbers or sequence exam items (MIT OpenCourseWare). For instance, in 4, 9, 14, … the constant difference is 5, so the next term is 19.

  2. Geometric Progressions (GP) -

    A GP features multiplication by a constant ratio r, with aₙ = a₝·r❿❻¹ to find any term in the series. Recognizing GP patterns is essential for sequence series quiz and number patterns test sections (University of Cambridge). For example, in 3, 6, 12, … the ratio is 2, so the fourth term is 24.

  3. Recursive Sequences & Fibonacci -

    Recursive sequences define each term based on previous ones, like the Fibonacci rule Fₙ = Fₙ₋₝ + Fₙ₋₂. Familiarity with this concept boosts your speed on numeric sequence challenge questions in iq test numbers assessments (Fibonacci Quarterly). A handy mnemonic is "add the last two" to get 1, 1, 2, 3, 5, 8, ….

  4. Difference Method for Polynomial Sequences -

    By computing first and second differences, you can detect linear, quadratic, and higher-order patterns in number sequences. This technique is crucial for acing sequence exam problems involving polynomial trends (Stanford Mathematics). For example, 2, 6, 12, 20, … has second differences constant at 2, indicating a quadratic pattern.

  5. Special Numeric Patterns -

    Key sequences include squares (n²), cubes (n³), primes, and triangular numbers (n(n+1)/2), all appearing frequently in number patterns test and sequence series quiz contexts. Memorizing formulas like "n² for squares" or using the prime sieve helps you recognize these quickly (Oxford University). For example, the squares sequence 1, 4, 9, 16, … uses n² for n=1,2,3,4.

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