In the following question, select the missing number from the given series.
60.75
Understanding the Number Series Pattern
The question asks us to find the missing number in the given series: 12, 18, 27, 40.5, ?
To solve number series problems, we need to identify the pattern or rule that governs the sequence of numbers.
Let's look at the relationship between consecutive terms:
- From 12 to 18: The difference is $18 - 12 = 6$. The ratio is $18 / 12 = 1.5$.
- From 18 to 27: The difference is $27 - 18 = 9$. The ratio is $27 / 18 = 1.5$.
- From 27 to 40.5: The difference is $40.5 - 27 = 13.5$. The ratio is $40.5 / 27 = 1.5$.
We can observe that the ratio between consecutive terms is constant, always 1.5. This indicates a pattern where each term is obtained by multiplying the previous term by 1.5. This type of series is a geometric progression with a common ratio of 1.5.
Calculating the Missing Number
Following the identified pattern, the next number in the series will be obtained by multiplying the last given term, 40.5, by 1.5.
Calculation:
Missing Number $= 40.5 \times 1.5$
Let's perform the multiplication:
$\quad 40.5$
$\times \quad 1.5$
-----
$\quad 2025$ (40.5 * 5)
$4050$ (40.5 * 10)
-----
$60.75$ (Summing the results, remembering decimal places)
So, the missing number is 60.75.
Summary of the Series and Pattern
| Term | Value | Pattern Applied |
|---|---|---|
| 1st | 12 | - |
| 2nd | 18 | $12 \times 1.5 = 18$ |
| 3rd | 27 | $18 \times 1.5 = 27$ |
| 4th | 40.5 | $27 \times 1.5 = 40.5$ |
| 5th | ? | $40.5 \times 1.5 = 60.75$ |
The calculated missing number, 60.75, matches one of the given options.
Revision Table: Key Concepts
| Concept | Description | Relevance to Problem |
|---|---|---|
| Number Series | A sequence of numbers following a specific pattern or rule. | The core topic of the question. |
| Pattern Recognition | Identifying the relationship between terms (addition, subtraction, multiplication, division, exponents, etc.). | Essential skill to solve the problem. |
| Geometric Progression | A series where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. | The specific type of series found in this problem (common ratio 1.5). |
Additional Information: Types of Number Series
Number series questions can involve various patterns. Some common types include:
- Arithmetic Series: A constant difference between consecutive terms (e.g., 2, 4, 6, 8...).
- Geometric Series: A constant ratio between consecutive terms (as seen in this problem).
- Difference Series: The pattern is in the difference between consecutive terms (e.g., differences might form an arithmetic or geometric series).
- Mixed Series: Involving a combination of arithmetic and geometric operations, or alternating patterns.
- Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5...).
- Prime Number Series: A sequence of prime numbers (e.g., 2, 3, 5, 7, 11...).
Identifying the type of pattern is the first step to successfully solving number series problems.
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, ?
