Identifying the Odd One Out in a Number Sequence

The question asks us to find the number that does not fit the pattern in the given sequence: \(3, 7, 11, 15, 19, 22\). We need to analyze the relationship between the numbers to identify the outlier.

Method 1: Analyzing the Arithmetic Progression

Let's examine the difference between consecutive numbers in the sequence:

• \(7 - 3 = 4\)
• \(11 - 7 = 4\)
• \(15 - 11 = 4\)
• \(19 - 15 = 4\)

We observe that the first five numbers (\(3, 7, 11, 15, 19\)) follow a pattern of adding \(4\) to get the next number. This indicates an arithmetic progression with a common difference of \(4\). Now let's check the difference between the last two numbers:

• \(22 - 19 = 3\)

The difference here is \(3\), not \(4\). This breaks the established pattern.

Method 2: Checking Number Properties (Even/Odd)

Another way to find the odd one out is to look at the properties of the numbers themselves.

Let's list the numbers and identify if they are even or odd:

• \(3\) is odd.
• \(7\) is odd.
• \(11\) is odd.
• \(15\) is odd.
• \(19\) is odd.
• \(22\) is even.

In this sequence, all numbers except \(22\) are odd numbers. The number \(22\) is the only even number present.

Conclusion

Based on both methods of analysis:

• The sequence \(3, 7, 11, 15, 19\) follows an arithmetic progression with a common difference of \(4\). The number \(22\) does not fit this pattern as the difference \(22 - 19\) is \(3\).
• The number \(22\) is the only even number in a sequence of otherwise odd numbers.

Therefore, the odd one out in the sequence \(3, 7, 11, 15, 19, 22\) is \(22\).