20. Number System Based Series & Patterns

Number system based series & patterns: missing number series, pattern identification (difference, squares/cubes, primes, alternating), digit-based patterns, remainders/cyclicity patterns, SSC CGL level solved examples & practice with answers.

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1) SSC series ka fastest approach (checklist)

1. Difference check: consecutive terms ka difference constant? (Arithmetic)
2. Second difference check: differences me pattern? (Quadratic / squares)
3. Ratio check: constant multiply/divide? (Geometric)
4. Squares/Cubes: perfect squares/cubes, or ± adjustment
5. Primes / Fibonacci / triangular numbers
6. Alternating: odd terms one series, even terms another
7. Digit pattern: digit sum, reverse, last digit cycle, mod pattern

2) Type A: Simple difference series

Example 1

2, 5, 8, 11, 14, ?

• Difference = +3 constant ⇒ next = 14+3 = 17

3) Type B: Second difference / squares based

Example 2

1, 4, 9, 16, 25, ?

• Squares: 1²,2²,3²,4²,5² ⇒ next = 6² = 36

Example 3 (± adjustment)

2, 5, 10, 17, 26, ?

• Pattern: 1²+1, 2²+1, 3²+1, 4²+1, 5²+1 ⇒ next = 6²+1 = 37
• Or differences: +3,+5,+7,+9 ⇒ next +11 ⇒ 26+11=37

4) Type C: Cube / power series

Example 4

1, 8, 27, 64, ?

• Cubes: 1³,2³,3³,4³ ⇒ next = 5³ = 125

5) Type D: Prime number series

Example 5

2, 3, 5, 7, 11, 13, ?

• Primes in order ⇒ next prime = 17

6) Type E: Alternating series (odd/even positions)

Example 6

1, 4, 2, 8, 3, 16, 4, ?

• Odd positions: 1,2,3,4 (natural)
• Even positions: 4,8,16,? (×2)
• Next even = 32 ⇒ answer = 32

7) Type F: Digit-based pattern (digit sum / last digit)

Example 7 (digit sum)

19, 28, 37, 46, 55, ?

• Each term +9 ⇒ next = 64
• Digit sum also constant: 1+9=10, 2+8=10,... ⇒ next should have digit sum 10 and follow +9 ⇒ 64

Example 8 (mod / last digit cycle)

2, 4, 8, 6, 2, 4, 8, 6, ?

• Last digit cycle of powers of 2 ⇒ pattern repeats (2,4,8,6)
• Next = 2

8) Type G: Mixed pattern (common SSC)

Example 9

3, 6, 12, 24, 48, ?

• ×2 each time ⇒ next = 96

Example 10

5, 6, 8, 11, 15, ?

• Differences: +1, +2, +3, +4 ⇒ next +5 ⇒ 15+5 = 20

9) Common traps

• Single rule nahi mil raha to alternating (odd/even split) जरूर check karo.
• Difference + squares adjustment: +3,+5,+7... type common hai.
• Digit patterns: digit sum constant, reverse, last digit cycles are frequent.

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10) Practice (SSC CGL) + Answers

1. 4, 9, 16, 25, 36, ?
2. 7, 10, 15, 22, 31, ?
3. 2, 6, 18, 54, ?
4. 1, 3, 6, 10, 15, ?
5. 2, 5, 11, 23, 47, ?
6. 8, 4, 2, 1, 0.5, ?

Show Answers

1. Squares: 2²,3²,4²,5²,6² ⇒ next 7² = 49
2. Differences: +3,+5,+7,+9 ⇒ next +11 ⇒ 31+11 = 42
3. ×3 each time ⇒ next = 54×3 = 162
4. Triangular numbers: +2,+3,+4,+5 ⇒ next +6 ⇒ 15+6 = 21
5. Pattern: ×2 +1 ⇒ 2→5→11→23→47→ 95
6. ÷2 each time ⇒ next = 0.25