Identifying the Odd One Out in the Number Sequence

The question asks us to identify the number that does not fit the pattern in the given sequence: 38, 57, 76, 95, 118.

Analyzing the Sequence Pattern

Let's examine the relationship between consecutive numbers in the sequence to find a consistent pattern.

Step 1: Calculate the differences between consecutive terms

• Difference between 57 and 38: \(57 - 38 = 19\)
• Difference between 76 and 57: \(76 - 57 = 19\)
• Difference between 95 and 76: \(95 - 76 = 19\)
• Difference between 118 and 95: \(118 - 95 = 23\)

Step 2: Identify the pattern

We observe that the first three differences are constant (\(19\)). This suggests an arithmetic progression where each term is obtained by adding \(19\) to the previous term.

• \(38 + 19 = 57\)
• \(57 + 19 = 76\)
• \(76 + 19 = 95\)

Following this pattern, the next term should be:

• \(95 + 19 = 114\)

Step 3: Compare with the given sequence

The sequence provided is 38, 57, 76, 95, 118. According to the identified pattern (adding 19), the term following 95 should be 114. However, the sequence lists 118 instead.

The number \(118\) deviates from this established pattern.

Alternative Pattern Analysis (Multiples of 19)

Let's check if the numbers are related to multiples of \(19\).

• \(38 = 2 \times 19\)
• \(57 = 3 \times 19\)
• \(76 = 4 \times 19\)
• \(95 = 5 \times 19\)

The pattern here is that the terms are multiples of \(19\), starting from \(2 \times 19\). The sequence of multipliers is \(2, 3, 4, 5\). The next multiplier should be \(6\).

• Expected next term: \(6 \times 19 = 114\)

Again, the given term \(118\) does not fit this pattern (\(118\) is not a multiple of \(19\)). Therefore, \(118\) is the odd one out.

Conclusion

Based on the analysis of the arithmetic progression (adding \(19\) consistently) or the pattern of multiples of \(19\), the number \(118\) is the one that does not belong to the sequence. The expected number in place of \(118\) would be \(114\).

The odd one out is 118.