What should come in place of the question mark (?) in the given series? 273, 263, 248, ?, 203
228
This question asks us to find the missing number in the given series: 273, 263, 248, ?, 203.
To solve number series problems, we typically look for a pattern in the relationship between consecutive terms. This could be addition, subtraction, multiplication, division, or a combination of operations, or patterns in the differences between terms.
Analysing the Number Series Pattern
Let's find the differences between the consecutive numbers we know:
- Difference between the 1st and 2nd term: \(263 - 273 = -10\)
- Difference between the 2nd and 3rd term: \(248 - 263 = -15\)
We have the differences -10 and -15. Let's look at the pattern in these differences. The difference decreased by 5 (from -10 to -15 is a change of -5).
Identifying the Pattern in Differences
It appears the pattern is that the amount being subtracted from each term is increasing by 5 each time. If this pattern continues, the next difference should be \(-15 - 5 = -20\).
So, to find the missing number (which is the 4th term), we should subtract 20 from the 3rd term:
- Missing Term (4th term) = 3rd term + (Next Difference)
- Missing Term = \(248 + (-20)\)
- Missing Term = \(248 - 20\)
- Missing Term = \(228\)
Verifying the Pattern
Now let's check if the pattern holds for the next step, from the 4th term (which we found as 228) to the 5th term (203). The difference should follow the pattern: the difference after -20 should be \(-20 - 5 = -25\).
- Difference between the 4th and 5th term: \(203 - 228 = -25\)
Since the calculated difference is -25, this matches the expected pattern in the differences (-10, -15, -20, -25). The pattern is consistent.
Confirming the Missing Number
The series with the missing number filled in is 273, 263, 248, 228, 203.
The differences are:
| Terms | Value | Difference from previous term |
|---|---|---|
| 1st | 273 | - |
| 2nd | 263 | \(263 - 273 = -10\) |
| 3rd | 248 | \(248 - 263 = -15\) |
| 4th (?) | 228 | \(228 - 248 = -20\) |
| 5th | 203 | \(203 - 228 = -25\) |
The pattern of differences -10, -15, -20, -25 is clear, where each difference is 5 less than the previous one.
Therefore, the missing number in the series is 228.
Revision Table: Number Series Concepts
| Concept | Description | Example |
|---|---|---|
| Arithmetic Series | Each term is obtained by adding or subtracting a constant value (common difference) to the previous term. | 2, 5, 8, 11... (common difference = 3) |
| Geometric Series | Each term is obtained by multiplying or dividing the previous term by a constant value (common ratio). | 3, 6, 12, 24... (common ratio = 2) |
| Difference Series | The pattern is found by looking at the differences between consecutive terms. Sometimes, the pattern is in the differences themselves, or in the differences of the differences (second-order differences). This question uses a first-order difference series pattern. | 1, 2, 4, 7, 11... Differences are 1, 2, 3, 4... |
| Mixed Series | A series that combines different types of patterns, or alternates between different operations. | 2, 4, 3, 9, 4, 16... (\(\times 2\), \(-1\), \(\times 3\), \(-5\), \(\times 4\)... or maybe squares: \(\sqrt{4}=2, \sqrt{9}=3, \sqrt{16}=4\)) |
Additional Information on Series Completion
Solving number series problems is a common part of logical reasoning and quantitative aptitude tests. The key is to systematically look for patterns. Here are some tips:
- Always calculate the differences between consecutive terms first. This is the most common type of pattern.
- If the first differences don't show a clear pattern, calculate the differences of the differences (second-order differences).
- Consider ratios if the numbers are growing or shrinking rapidly (geometric series).
- Look for patterns involving squares, cubes, prime numbers, or other special sequences.
- Sometimes the series might be an alternating series, where different rules apply to alternate terms.
- Practice with various types of series helps in quickly identifying potential patterns.
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, ?
