Identify the number that does NOT belong to the following series. 49, 98, 196, 394, 784, 1568
394
Analyzing the Number Series Pattern
The question asks us to identify the number that does not fit the pattern in the given series: 49, 98, 196, 394, 784, 1568.
To solve this, let's examine the relationship between consecutive numbers in the series. We can try simple arithmetic operations like addition, subtraction, multiplication, or division.
Discovering the Pattern in the Series
Let's look at the first few terms:
- From 49 to 98: $98 \div 49 = 2$. This suggests multiplication by 2.
- From 98 to 196: $196 \div 98 = 2$. This also suggests multiplication by 2.
The pattern appears to be that each term after the first is obtained by multiplying the previous term by 2.
Applying the Pattern to the Series
Let's apply this rule to the entire series and see which number deviates:
- First term: 49
- Second term: $49 \times 2 = 98$ (Matches the given series)
- Third term: $98 \times 2 = 196$ (Matches the given series)
- Fourth term: $196 \times 2 = 392$. The given number is 394. This does not match.
- Fifth term: If the correct fourth term was 392, then $392 \times 2 = 784$ (Matches the given series)
- Sixth term: $784 \times 2 = 1568$ (Matches the given series)
Based on the pattern of multiplying by 2, the fourth term should be 392, not 394.
Identifying the Misfit Number
The number that disrupts the established pattern ($ \times 2$) is 394. It should have been 392 if the pattern were consistent throughout the series.
Therefore, 394 is the number that does NOT belong to the given series.
Revision Table: Series Analysis
| Term Number | Given Number | Expected Number (Pattern: $\times 2$) | Matches Pattern? |
|---|---|---|---|
| 1st | 49 | 49 | Yes |
| 2nd | 98 | $49 \times 2 = 98$ | Yes |
| 3rd | 196 | $98 \times 2 = 196$ | Yes |
| 4th | 394 | $196 \times 2 = 392$ | No |
| 5th | 784 | $392 \times 2 = 784$ | Yes (based on expected 4th term) |
| 6th | 1568 | $784 \times 2 = 1568$ | Yes |
Additional Information on Number Series
Number series problems often involve finding a pattern that relates consecutive terms. Common patterns include:
- Arithmetic Progression: Adding or subtracting a constant value.
- Geometric Progression: Multiplying or dividing by a constant value.
- Differences or Ratios: The difference or ratio between consecutive terms forms another recognizable pattern (e.g., an arithmetic or geometric series).
- Squaring or Cubing: Terms might be related to squares, cubes, or their roots.
- Combinations: A mix of operations, e.g., multiply by 2 then add 1.
- Fibonacci Sequence: Each term is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...).
Identifying the pattern is key to solving number series questions. It often requires checking for simple patterns first and then moving to more complex ones if necessary.
Important Questions from Number Series
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Select the number from among the given options that can replace the question mark (?) in the following series.
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