The question asks to identify the term that does not belong in the series: 2T3, 5S6, 11R9, 16Q12, 23P15. We need to find the pattern governing the series.

Analyze Series Components

Each term in the series consists of three parts: a first number, a letter, and a second number. Let's analyze the pattern for each part separately.

Second Number Pattern

• The sequence of second numbers is: 3, 6, 9, 12, 15.
• Calculating the difference between consecutive terms: $6 - 3 = 3$, $9 - 6 = 3$, $12 - 9 = 3$, $15 - 12 = 3$.
• This forms an arithmetic progression with a common difference of 3. This pattern is consistent across all terms.

Letter Pattern

• The sequence of letters is: T, S, R, Q, P.
• These are consecutive letters in reverse alphabetical order. This pattern is consistent across all terms.
• The corresponding alphabetical positions are: 20, 19, 18, 17, 16.

First Number Pattern

• The sequence of first numbers is: 2, 5, 11, 16, 23.
• Calculating the difference between consecutive terms:
  • $5 - 2 = 3$
  • $11 - 5 = 6$
  • $16 - 11 = 5$
  • $23 - 16 = 7$
• The differences (3, 6, 5, 7) do not form a simple arithmetic or geometric progression, indicating an inconsistency here.

Identify the Outlier

Since the second number and letter patterns are consistent across all terms, the anomaly must lie within the first number sequence (2, 5, 11, 16, 23).

Let's examine the pattern suggested by the first three first numbers (2, 5, 11). The increments are 3 and 6. This suggests a pattern where the increment doubles each time: 3, 6, 12, 24, ...

Using this doubling increment pattern, the expected sequence for the first numbers would be:

• Term 1: 2
• Term 2: $2 + 3 = 5$
• Term 3: $5 + 6 = 11$
• Term 4: $11 + 12 = 23$
• Term 5: $23 + 24 = 47$

The expected sequence is 2, 5, 11, 23, 47. Comparing this with the given first numbers (2, 5, 11, 16, 23):

• The numbers 2, 5, and 11 match the pattern.
• The fourth term in the given series is 16Q12. Its first number is 16. According to the pattern, the expected first number for the fourth position (corresponding to letter Q) is 23. Thus, 16 breaks the pattern.
• The fifth term is 23P15. Its first number is 23. According to the pattern, the expected first number for the fifth position (corresponding to letter P) is 47.

The term 16Q12 is the one that does not belong because its first number (16) deviates from the established doubling increment pattern required for the first numbers.