Understanding the Number Series Pattern

The question asks us to find the number that does not fit into the given series: 5, 9, 17, 29, 55, 65. To solve this type of number series problem, we need to look for a pattern between consecutive terms.

Let's examine the differences between the numbers in the series:

• Difference between the 2nd and 1st term: $\text{9 - 5 = 4}$
• Difference between the 3rd and 2nd term: $\text{17 - 9 = 8}$
• Difference between the 4th and 3rd term: $\text{29 - 17 = 12}$
• Difference between the 5th and 4th term: $\text{55 - 29 = 26}$
• Difference between the 6th and 5th term: $\text{65 - 55 = 10}$

The sequence of differences is: 4, 8, 12, 26, 10.

Identifying the Pattern in Differences

Let's look for a pattern in these differences (4, 8, 12, 26, 10). Notice the first three differences:

• 4 to 8: adds 4 ($\text{8 - 4 = 4}$)
• 8 to 12: adds 4 ($\text{12 - 8 = 4}$)

This suggests that the differences might be increasing by 4 each time. Let's assume this pattern continues for the entire series of differences.

Expected sequence of differences:

• Starting difference: 4
• Next difference: $\text{4 + 4 = 8}$
• Next difference: $\text{8 + 4 = 12}$
• Next difference: $\text{12 + 4 = 16}$
• Next difference: $\text{16 + 4 = 20}$

So, the expected differences should be 4, 8, 12, 16, 20.

Constructing the Expected Number Series

Now, let's use this expected pattern of differences to build the number series starting from the first term, 5:

• 1st term: 5
• 2nd term: $\text{5 + 4 = 9}$ (Matches the given series)
• 3rd term: $\text{9 + 8 = 17}$ (Matches the given series)
• 4th term: $\text{17 + 12 = 29}$ (Matches the given series)
• 5th term: $\text{29 + 16 = 45}$ (Expected term)
• 6th term: $\text{45 + 20 = 65}$ (Matches the given series)

The expected number series based on the identified pattern is: 5, 9, 17, 29, 45, 65.

Comparing Given Series and Expected Series

Let's compare the given series with the expected series:

We can clearly see that the fifth term in the given series is 55, while the expected fifth term based on the pattern is 45.

Identifying the Outlier Number

Therefore, the number 55 does not follow the pattern of the series. It is the number that does NOT belong.

Revision Table: Number Series Pattern

Additional Information: Solving Number Series

When trying to find the outlier or the next term in a number series, consider these common patterns:

• Arithmetic Progression: A constant difference between terms.
• Geometric Progression: A constant ratio between terms.
• Difference Series: The differences between consecutive terms form a recognizable pattern (like an arithmetic or geometric progression, or even another series based on differences). This is the pattern we saw here.
• Ratio Series: The ratio between consecutive terms forms a recognizable pattern.
• Mixed Series: Combination of two or more simple series.
• Fibonacci-like Series: Each term is the sum of the previous two terms.
• Powers or Squares/Cubes: Terms related to squares, cubes, or other powers of numbers.

Always calculate the differences (and sometimes differences of differences) first, as this is a very common pattern in numerical reasoning questions.