Number series questions involve a sequence of numbers where you need to identify the pattern or rule governing the sequence. Sometimes, one or more numbers are missing, and you have to figure out the missing numbers based on the pattern.
Here are the most common types of number series:
| Type | Formula | Example |
|---|---|---|
| Prime Number Series | 2, 3, 5, 7, 11, 13, ... | Next prime number after 13 is 17. |
| Difference Series | Difference between numbers is constant. | 2, 5, 8, 11, 14, ... (Difference = 3) |
| Multiplication Series | Each number is multiplied by a constant. | 2, 6, 18, 54, ... (Multiply by 3) |
| Square Series (n2) | 1, 4, 9, 16, 25, ... | Next number is 36 (62). |
| Cube Series (n3) | 1, 8, 27, 64, 125, ... | Next number is 216 (63). |
| Factorial Series | 1, 1, 2, 6, 24, 120, ... | Next number is 720 (6!). |
| Combination Series | Combination of operations like addition, subtraction, multiplication, etc. | 2, 4, 8, 16, 32, ... (Multiply by 2) |
Example: 0, 3, 8, 15, 24, 35, 48, ...
Solution: The series is 12-1, 22-1, 32-1, etc. The next number is 82-1 = 63.
Alternate Logic: The differences between numbers are 3, 5, 7, 9, 11, 13, etc. So, the next number is 48 + 15 = 63.
Example: 2, 5, 10, 17, 26, 37, ...
Solution: The series is 12+1, 22+1, 32+1, etc. The next number is 72+1 = 50.
Example 1: 720, 120, 24, ..., 2, 1
Solution: 720 ÷ 6 = 120, 120 ÷ 5 = 24, 24 ÷ 4 = 6, 6 ÷ 3 = 2, 2 ÷ 2 = 1.
Example 2: 32, 48, 72, 108, ..., 243
Solution: Each number is multiplied by 3/2. So, 32 × 3/2 = 48, 48 × 3/2 = 72, 72 × 3/2 = 108, 108 × 3/2 = 162.
Example: 2, 6, 12, 20, ..., 42
Solution: The series is 12+1, 22+2, 32+3, etc. The next number is 52+5 = 30.
Alternate Logic: The series is 1×2, 2×3, 3×4, 4×5. The next number is 5×6 = 30.
Example: 1, 8, 27, 64, 125, 216, ...
Solution: The series is 13, 23, 33, etc. The missing number is 73 = 343.
Example: 2, 9, 28, 65, 126, 217, 344, ...
Solution: The series is 13+1, 23+1, 33+1, etc. The missing number is 83+1 = 513.
Example: 0, 7, 26, 63, 124, ..., 342
Solution: The series is 13-1, 23-1, 33-1, etc. The missing number is 63-1 = 215.
Example: 2, 10, 30, 68, 130, ..., 350
Solution: The series is 13+1, 23+2, 33+3, etc. The missing number is 63+6 = 222.
Example: 0, 6, 24, 60, 120, 210, ...
Solution: The series is 13-1, 23-2, 33-3, etc. The missing number is 73-7 = 336.
Alternate Logic: The series is 0×1×2, 1×2×3, 2×3×4, etc. The missing number is 6×7×8 = 336.
Example: 2, 12, 36, 80, 150, ...
Solution: The series is 13+12, 23+22, 33+32, etc. The missing number is 63+62 = 252.
Example: 0, 4, 18, 48, 100, ...
Solution: The series is 13-12, 23-22, 33-32, etc. The missing number is 63-62 = 180.
Example: 48, 12, 76, 13, 54, 9, 32, ...
Solution: 4 + 8 = 12, 7 + 6 = 13, 5 + 4 = 9, 3 + 2 = 5.
Example: 1, 1, 2, 6, 24, 120, ...
Solution: The series is 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720.
Q1: What is the next number in the series: 2, 5, 10, 17, 26, ...?
Options: A) 35 B) 37 C) 39 D) 41
Answer: B) 37 (The series is n2 + 1, so 62 + 1 = 37).
Q2: What is the next number in the series: 1, 8, 27, 64, ...?
Options: A) 125 B) 100 C) 216 D) 343
Answer: A) 125 (The series is n3, so 53 = 125).
Q3: What is the next number in the series: 2, 4, 8, 16, 32, ...?
Options: A) 64 B) 48 C) 56 D) 72
Answer: A) 64 (Each number is multiplied by 2).
Number series questions can be tricky, but with practice and the right approach, you can solve them quickly. Remember to look for patterns, calculate differences, and use shortcuts to save time. Good luck!