NUMBER SERIES

 

🧠 Number Series: Complete Guide for SSC & Banking Exams

---

1️⃣ Introduction to Number Series

A Number Series is a sequence of numbers arranged in a particular order following a specific rule or pattern. In exams, you're usually asked to:

• Find the next number in the series
• Find the wrong number in the series

---

2️⃣ Types of Number Series (Basic to Advanced)

Type	Description	Example
Arithmetic Series (AP)	Constant addition/subtraction	5, 10, 15, 20
Geometric Series (GP)	Constant multiplication/division	2, 4, 8, 16
Square/Cube Series	Perfect squares or cubes	1, 4, 9, 16
Prime Number Series	Prime numbers in order	2, 3, 5, 7, 11
Fibonacci Series	Sum of the last two numbers	0, 1, 1, 2, 3
Alternating Pattern	Alternates between different operations	1, 4, 2, 5, 3, 6
Difference Pattern	Differences form a recognizable pattern	2, 5, 10, 17
Miscellaneous/Mixed	Combination of logic (e.g., +n², ×n, etc.)	1, 2, 4, 7, 11
Wrong Number Series	Identify a number that doesn’t fit the logic	2, 4, 8, 16, 33

---

3️⃣ Step-by-Step Approach to Solve Number Series

🧪 Step 1: Check for Common Difference

Try subtracting consecutive terms.

🧪 Step 2: Check for Common Ratio

If numbers are growing quickly, try division.

🧪 Step 3: Look for Squares, Cubes, Primes

Is the number a square, cube, or prime?

🧪 Step 4: Check for Alternating Patterns

Are odd and even positions behaving differently?

🧪 Step 5: Reverse Engineering

Sometimes it's easier to analyze from the last term backward.

---

4️⃣ Example Problems (With Explanations)

🔹 Type 1: Arithmetic Progression (AP)

Q1. 7, 14, 21, 28, ? → Answer: 35 (Add 7)

---

🔹 Type 2: Geometric Progression (GP)

Q2. 3, 6, 12, 24, ? → Answer: 48 (×2)

---

🔹 Type 3: Square Series

Q3. 1, 4, 9, 16, ? → Answer: 25 (Squares of 1,2,3...)

---

🔹 Type 4: Alternating Series

Q4. 10, 15, 13, 18, 16, ? → Answer: 21 (+5, -2)

---

🔹 Type 5: Prime Series

Q5. 2, 3, 5, 7, 11, ? → Answer: 13 (Prime numbers)

---

🔹 Type 6: Difference Pattern

Q6. 2, 5, 10, 17, 26, ? → Answer: 37 (Diffs +3, +5, +7…)

---

🔹 Type 7: Fibonacci Series

Q7. 0, 1, 1, 2, 3, 5, ? → Answer: 8 (Prev two sum)

---

🔹 Type 8: Cube Numbers

Q8. 1, 8, 27, 64, ? → Answer: 125 (Cubes)

---

🔹 Type 9: Decreasing Pattern

Q9. 1000, 500, 250, ? → Answer: 125 (÷2)

---

🔹 Type 10: Wrong Number

Q10. 2, 4, 8, 16, 33, 64 → Answer: 33 is wrong (Expected 32)

---

5️⃣ Common Tricks and Shortcuts

Tip	Explanation
Difference Table	Create difference table to observe patterns
Square/Cube Recognition	Memorize squares & cubes up to 25 & 15 respectively
Ratio Check	For rapid growth, check for GP
Prime Number Recall	Learn first 50 primes for reference
Alternate Number Check	Divide series into odd/even positions

---

6️⃣ Mistakes to Avoid

• Don’t assume it’s AP/GP immediately
• Don’t ignore alternating sequences
• Always consider primes, squares, cubes
• Don’t rush — verify each step

---

 

 

 

7️⃣ Practice Questions (Basic to Advanced)

Here are a few practice problems for warm-up:

1. 11, 13, 17, 19, 23, ?
2. 64, 32, 16, 8, 4, ?
3. 1, 3, 6, 10, 15, ?
4. 4, 9, 16, 25, ?
5. 3, 5, 9, 17, 33, ?

8️⃣ Daily Practice Plan for Students

Day	Focus Area	Practice
1	AP, GP, Squares	20 Qs
2	Cubes, Fibonacci, Prime	20 Qs
3	Alternating, Difference Series	20 Qs
4	Mixed Patterns	20 Qs
5	Wrong Number Series	20 Qs
6	Mock Test (Full Section)	1 Paper
7	Revision & Speed Improvement	40 Qs

---

9️⃣ Best Resources for Practice

• ✅ Smartkeeda – Topic-wise quizzes
• ✅ Testbook – PYQs and solutions
• ✅ BankersAdda – Banking-specific sets
• ✅ Unacademy – Free concept classes
• ✅ GeeksforGeeks Reasoning – Logical explanations

---

 

 

🔟 Summary

• Start with basic types → AP, GP, Squares, etc.
• Understand patterns → Differences, Ratios, Alternating
• Practice regularly → Build speed & accuracy
• Use error logs → Track and analyze mistakes
• Refer to quality resources & take mock tests

 

50 Number Series Practice Questions

---

Level 1: Easy (1–15)

1. 2, 4, 6, 8, ?
   Answer: 10 (Add 2)
2. 5, 10, 15, 20, ?
   Answer: 25 (Add 5)
3. 1, 3, 5, 7, ?
   Answer: 9 (Add 2)
4. 3, 9, 27, 81, ?
   Answer: 243 (×3)
5. 10, 20, 40, 80, ?
   Answer: 160 (×2)
6. 1, 4, 9, 16, ?
   Answer: 25 (Squares of natural numbers)
7. 2, 6, 12, 20, ?
   Answer: 30 (Add consecutive even numbers: +4, +6, +8...)
8. 0, 1, 1, 2, 3, 5, ?
   Answer: 8 (Fibonacci series)
9. 100, 90, 80, 70, ?
   Answer: 60 (Subtract 10)
10. 1, 8, 27, 64, ?
    Answer: 125 (Cubes of natural numbers)
11. 2, 5, 10, 17, ?
    Answer: 26 (Add consecutive odd numbers: +3, +5, +7...)
12. 81, 27, 9, 3, ?
    Answer: 1 (Divide by 3)
13. 11, 13, 17, 19, 23, ?
    Answer: 29 (Prime numbers)
14. 7, 14, 28, 56, ?
    Answer: 112 (×2)
15. 4, 7, 10, 13, ?
    Answer: 16 (Add 3)

---

Level 2: Medium (16–35)

16. 5, 6, 8, 11, 15, ?
    Answer: 20 (Add +1, +2, +3, +4...)
17. 2, 3, 5, 8, 13, ?
    Answer: 21 (Fibonacci series)
18. 1, 3, 9, 27, ?
    Answer: 81 (×3)
19. 16, 13, 10, 7, ?
    Answer: 4 (Subtract 3)
20. 2, 12, 30, 56, ?
    Answer: 90 (Add 10, 18, 26, 34...)
21. 1, 2, 6, 24, 120, ?
    Answer: 720 (Factorials: 1!, 2!, 3!, 4!, 5!, 6!)
22. 1, 4, 5, 8, 9, 12, ?
    Answer: 13 (Alternate +3 and +1)
23. 100, 80, 60, 40, ?
    Answer: 20 (Subtract 20)
24. 3, 9, 27, 54, ?
    Answer: 81 (×3, then ×3/2 alternately — here, just ×1.5)
25. 7, 10, 8, 11, 9, ?
    Answer: 12 (Add 3, subtract 2 alternately)
26. 1, 8, 27, 64, 125, ?
    Answer: 216 (Cubes)
27. 2, 4, 12, 48, ?
    Answer: 240 (Multiply by 2, 3, 4...)
28. 2, 4, 7, 11, 16, ?
    Answer: 22 (Add 2, 3, 4, 5...)
29. 12, 11, 13, 12, 14, ?
    Answer: 13 (Alternating -1 and +2)
30. 1, 3, 6, 10, 15, ?
    Answer: 21 (Triangular numbers)
31. 15, 30, 60, 120, ?
    Answer: 240 (Multiply by 2)
32. 1000, 500, 250, 125, ?
    Answer: 62.5 (Divide by 2)
33. 1, 1, 2, 6, 24, 120, ?
    Answer: 720 (Factorials)
34. 6, 11, 21, 36, 56, ?
    Answer: 81 (Differences: +5, +10, +15, +20...)
35. 5, 7, 11, 19, 35, ?
    Answer: 67 (Double previous minus 3)

---

Level 3: Hard (36–50)

36. 4, 6, 9, 6, 11, 6, 13, ?
    Answer: 6 (Alternate increasing odd numbers and 6)
37. 5, 10, 20, 40, 70, ?
    Answer: 110 (Add 5, 10, 20, 30, 40)
38. 3, 6, 18, 72, ?
    Answer: 360 (Multiply by 2, 3, 4, 5...)
39. 1, 4, 9, 16, 25, 36, ?
    Answer: 49 (Squares)
40. 10, 14, 18, 24, 32, ?
    Answer: 42 (Differences +4, +4, +6, +8, +10)
41. 7, 8, 10, 13, 17, ?
    Answer: 22 (Differences +1, +2, +3, +4, +5)
42. 1, 2, 6, 24, 120, 720, ?
    Answer: 5040 (Factorials)
43. 2, 5, 10, 17, 26, ?
    Answer: 37 (Add consecutive odd numbers)
44. 10, 30, 90, 270, ?
    Answer: 810 (×3)
45. 4, 7, 15, 31, 63, ?
    Answer: 127 (×2 - 1)
46. 1, 3, 7, 13, 21, ?
    Answer: 31 (Add 2, 4, 6, 8, 10)
47. 100, 90, 70, 40, ?
    Answer: 0 (Subtract 10, 20, 30, 40...)
48. 1, 3, 8, 15, 24, ?
    Answer: 35 (Add consecutive squares: +2, +5, +7, +9, +11)
49. 6, 11, 21, 36, 56, ?
    Answer: 81 (Add 5, 10, 15, 20, 25)
50. 2, 6, 12, 20, 30, ?
    Answer: 42 (Add consecutive even numbers: +4, +6, +8...)