In the following question, select the missing number from the given series.
236
Finding the Missing Number in a Series
The question asks us to find the missing number in the given series: 11, 12, 20, 47, 111, ?.
To solve number series questions, we look for a pattern between consecutive terms. Let's examine the differences between the terms:
- Difference between the 2nd and 1st term: ${12 - 11 = 1}$
- Difference between the 3rd and 2nd term: ${20 - 12 = 8}$
- Difference between the 4th and 3rd term: ${47 - 20 = 27}$
- Difference between the 5th and 4th term: ${111 - 47 = 64}$
Let's list the differences we found:
${1, 8, 27, 64, \dots}$
Now, let's try to identify the pattern in these differences. We can observe that these numbers are perfect cubes:
- ${1 = 1 \times 1 \times 1 = 1^3}$
- ${8 = 2 \times 2 \times 2 = 2^3}$
- ${27 = 3 \times 3 \times 3 = 3^3}$
- ${64 = 4 \times 4 \times 4 = 4^3}$
The pattern of the differences is the cube of consecutive natural numbers starting from 1. The differences are ${1^3, 2^3, 3^3, 4^3, \dots}$.
Following this pattern, the next difference in the series should be ${5^3}$.
Let's calculate the value of ${5^3}$:
${5^3 = 5 \times 5 \times 5 = 125}$
So, the missing number is obtained by adding this next difference (125) to the last given term (111).
Missing number ${= \text{Last term} + \text{Next difference}}$
Missing number ${= 111 + 125}$
Missing number ${= 236}$
Therefore, the missing number in the series is 236.
The complete series is 11, 12, 20, 47, 111, 236.
Breakdown of the Number Series Pattern
| Term | Value | Difference from previous term | Pattern of Difference |
|---|---|---|---|
| 1st | 11 | - | - |
| 2nd | 12 | ${12 - 11 = 1}$ | ${1 = 1^3}$ |
| 3rd | 20 | ${20 - 12 = 8}$ | ${8 = 2^3}$ |
| 4th | 47 | ${47 - 20 = 27}$ | ${27 = 3^3}$ |
| 5th | 111 | ${111 - 47 = 64}$ | ${64 = 4^3}$ |
| 6th | ? | Next difference is ${5^3 = 125}$ | ${125 = 5^3}$ |
The missing number is ${111 + 125 = 236}$.
Revision Table: Understanding Number Series
| Type of Pattern | Description | Example |
|---|---|---|
| Arithmetic Progression | Constant difference between terms. | 2, 4, 6, 8, ... (Difference = 2) |
| Geometric Progression | Constant ratio between terms. | 3, 9, 27, 81, ... (Ratio = 3) |
| Difference Series | The differences between terms follow a pattern (e.g., arithmetic, geometric, squares, cubes). | 1, 2, 4, 7, 11, ... (Differences: 1, 2, 3, 4) |
| Mixed Series | Combination of different patterns (e.g., alternating arithmetic and geometric operations). | 5, 10, 7, 14, 11, 22, ... (x2, -3, x2, -3, ...) |
| Series based on Squares/Cubes | Terms or differences related to squares or cubes of numbers. | This question is an example where differences are cubes. |
Additional Information on Solving Number Series Questions
Solving number series problems requires careful observation and pattern recognition. Here are some common strategies:
- Calculate Differences: Find the differences between consecutive terms. If the differences are constant, it's an arithmetic series. If not, look for a pattern in the differences themselves (first level difference, second level difference, etc.).
- Calculate Ratios: Find the ratio between consecutive terms. If the ratio is constant, it's a geometric series.
- Look for Squares and Cubes: Check if terms are perfect squares, cubes, or related to squares/cubes (e.g., $n^2 \pm k$, $n^3 \pm k$).
- Identify Alternating Patterns: Sometimes, two different patterns alternate within the series.
- Look for Combined Operations: The pattern might involve a combination of arithmetic and multiplication/division operations.
- Prime Numbers: The series might involve prime numbers or operations related to them.
- Fibonacci-like Series: Each term might be the sum of the previous two terms (or a variation).
Practicing different types of number series helps in quickly identifying the underlying pattern.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
