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30 Number Series Questions and Answers

30 solved Number Series questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced number series questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

Arithmetic progression: Tn = a + (n-1)d, Sum = n/2[2a + (n-1)d] Geometric progression: Tn = a × r^(n-1) Check differences first, then ratios, then squares/cubes Alternating series: check even/odd position patterns separately
Q1 Medium

Find the next number: 15, 23, 8, 28, 17, 36, ?

  • A. 21
  • B. 19 ✓
  • C. 17
  • D. 15
Explanation: Odd positions follow +2 sequence. Next odd-position term is 19.
Q2 Medium

Find the next number in the pattern: 3, 9, 27, 81, 243, ?

  • A. 724
  • B. 729 ✓
  • C. 719
  • D. 734
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 3. Next = 243 x 3 = 729.
Q3 Medium

Find the next number: 7, 32, 13, 27, 13, 38, ?

  • A. 15 ✓
  • B. 17
  • C. 13
  • D. 11
Explanation: Odd positions follow +2 sequence. Next odd-position term is 15.
Q4 Medium

Find the next number in the pattern: 2, 6, 18, 54, 162, ?

  • A. 491
  • B. 481
  • C. 486 ✓
  • D. 476
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 3. Next = 162 x 3 = 486.
Q5 Medium

Find the next number: 4, 13, 22, 31, 40, ?

  • A. 47
  • B. 49 ✓
  • C. 51
  • D. 46
Explanation: Arithmetic progression with common difference 9. Next = 49.
Q6 Medium

Find the next number: 15, 29, 9, 29, 9, 29, ?

  • A. 7
  • B. 11 ✓
  • C. 13
  • D. 9
Explanation: Odd positions follow +2 sequence. Next odd-position term is 11.
Q7 Medium

Find the next number in the pattern: 5, 10, 20, 40, 80, ?

  • A. 150
  • B. 155
  • C. 165
  • D. 160 ✓
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 2. Next = 80 x 2 = 160.
Q8 Medium

Find the next number: 13, 24, 17, 24, 10, 37, ?

  • A. 14
  • B. 12 ✓
  • C. 8
  • D. 10
Explanation: Odd positions follow +2 sequence. Next odd-position term is 12.
Q9 Medium

Find the next number: 10, 17, 24, 31, 38, ?

  • A. 45 ✓
  • B. 42
  • C. 43
  • D. 47
Explanation: Arithmetic progression with common difference 7. Next = 45.
Q10 Medium

Find the next number: 13, 24, 17, 24, 9, 31, ?

  • A. 13
  • B. 7
  • C. 11 ✓
  • D. 9
Explanation: Odd positions follow +2 sequence. Next odd-position term is 11.
Q11 Medium

Find the next number in the pattern: 2, 4, 8, 16, 32, ?

  • A. 64 ✓
  • B. 69
  • C. 54
  • D. 59
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 2. Next = 32 x 2 = 64.
Q12 Medium

Find the next number: 15, 28, 14, 29, 13, 30, ?

  • A. 17
  • B. 15 ✓
  • C. 13
  • D. 11
Explanation: Odd positions follow +2 sequence. Next odd-position term is 15.
Q13 Medium

Find the next number in the pattern: 4, 8, 16, 32, 64, ?

  • A. 118
  • B. 133
  • C. 128 ✓
  • D. 123
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 2. Next = 64 x 2 = 128.
Q14 Medium

Find the next number: 5, 22, 12, 28, 10, 33, ?

  • A. 14
  • B. 12 ✓
  • C. 8
  • D. 10
Explanation: Odd positions follow +2 sequence. Next odd-position term is 12.
Q15 Medium

Find the next number: 8, 13, 18, 23, 28, ?

  • A. 33 ✓
  • B. 30
  • C. 31
  • D. 35
Explanation: Arithmetic progression with common difference 5. Next = 33.
Q16 Medium

Find the next number: 7, 22, 10, 30, 9, 29, ?

  • A. 9
  • B. 13
  • C. 7
  • D. 11 ✓
Explanation: Odd positions follow +2 sequence. Next odd-position term is 11.
Q17 Medium

Find the next number in the pattern: 4, 12, 36, 108, 324, ?

  • A. 967
  • B. 962
  • C. 972 ✓
  • D. 977
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 3. Next = 324 x 3 = 972.
Q18 Medium

Find the next number: 5, 21, 10, 28, 14, 26, ?

  • A. 12
  • B. 14
  • C. 18
  • D. 16 ✓
Explanation: Odd positions follow +2 sequence. Next odd-position term is 16.
Q19 Medium

Find the next number: 4, 9, 14, 19, 24, ?

  • A. 31
  • B. 29 ✓
  • C. 26
  • D. 27
Explanation: Arithmetic progression with common difference 5. Next = 29.
Q20 Medium

Find the next number: 12, 27, 8, 33, 12, 29, ?

  • A. 10
  • B. 16
  • C. 14 ✓
  • D. 12
Explanation: Odd positions follow +2 sequence. Next odd-position term is 14.
Q21 Medium

Find the next number: 15, 22, 29, 36, 43, ?

  • A. 52
  • B. 48
  • C. 50 ✓
  • D. 47
Explanation: Arithmetic progression with common difference 7. Next = 50.
Q22 Medium

Find the next number: 5, 25, 10, 30, 19, 27, ?

  • A. 23
  • B. 17
  • C. 21 ✓
  • D. 19
Explanation: Odd positions follow +2 sequence. Next odd-position term is 21.
Q23 Medium

Find the next number: 7, 16, 25, 34, 43, ?

  • A. 54
  • B. 49
  • C. 52 ✓
  • D. 50
Explanation: Arithmetic progression with common difference 9. Next = 52.
Q24 Medium

Find the next number: 5, 21, 16, 31, 18, 36, ?

  • A. 20 ✓
  • B. 16
  • C. 22
  • D. 18
Explanation: Odd positions follow +2 sequence. Next odd-position term is 20.
Q25 Medium

Find the next number: 5, 10, 15, 20, 25, ?

  • A. 27
  • B. 28
  • C. 30 ✓
  • D. 32
Explanation: Arithmetic progression with common difference 5. Next = 30.
Q26 Medium

Find the next number: 8, 28, 13, 31, 14, 29, ?

  • A. 18
  • B. 16 ✓
  • C. 14
  • D. 12
Explanation: Odd positions follow +2 sequence. Next odd-position term is 16.
Q27 Medium

Find the next number: 12, 16, 20, 24, 28, ?

  • A. 29
  • B. 30
  • C. 32 ✓
  • D. 34
Explanation: Arithmetic progression with common difference 4. Next = 32.
Q28 Medium

Find the next number in the pattern: 3, 6, 12, 24, 48, ?

  • A. 86
  • B. 91
  • C. 96 ✓
  • D. 101
Explanation: For number series, first find the difference between consecutive terms. If the differences form a pattern, that reveals the rule. Check for arithmetic, geometric, or square/cube patterns. Geometric progression with ratio 2. Next = 48 x 2 = 96.
Q29 Medium

Find the next number: 11, 15, 19, 23, 27, ?

  • A. 33
  • B. 29
  • C. 31 ✓
  • D. 28
Explanation: Arithmetic progression with common difference 4. Next = 31.
Q30 Medium

Find the next number: 6, 28, 16, 31, 11, 29, ?

  • A. 13 ✓
  • B. 15
  • C. 9
  • D. 11
Explanation: Odd positions follow +2 sequence. Next odd-position term is 13.

Key Takeaways

  • Always check differences first — they reveal the underlying pattern.
  • If differences don't help, check ratios between consecutive terms.
  • Look for alternating patterns, square/cube sequences, or combined rules.
  • Practice is key: the more patterns you see, the faster you recognize them.

Frequently Asked Questions

How do I solve number series questions?

First check the difference between consecutive terms. If differences form a pattern (constant, increasing, or themselves a series), that reveals the rule. If not, check ratios. If neither works, look for alternating patterns, squares, cubes, or combination rules.

What are common number series patterns?

Arithmetic (+/- constant), Geometric (×/÷ constant), Square/Cube patterns, Fibonacci-like (sum of previous two), Alternating (two interleaved series), and Mixed (combination of arithmetic and geometric).

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