Analyzing the Series Pattern

The series consists of fractions that alternate between a Letter/Number format and a Number/Letter format. Let's break down the structure:

• Term 1: $\displaystyle \frac{\text{D}}{23}$ (Letter/Number)
• Term 2: $\displaystyle \frac{20}{\text{G}}$ (Number/Letter)
• Term 3: $\displaystyle \frac{\text{J}}{17}$ (Letter/Number)
• Term 4: $\displaystyle \frac{14}{\text{M}}$ (Number/Letter)
• Term 5: $\displaystyle \frac{\text{P}}{11}$ (Letter/Number)
• Term 6: $\displaystyle \frac{\text{?}}{\text{?}}$ (This term should follow the Number/Letter pattern)

Numerator Progression

Let's analyze the sequence of numerators: D, 20, J, 14, P, ?

Convert letters to their corresponding numerical positions in the alphabet (A=1, B=2, ..., Z=26): 4, 20, 10, 14, 16, ?

We observe two interleaved patterns:

• Numerators at odd positions (1st, 3rd, 5th): D (4), J (10), P (16). This sequence increases by 6 each time (4 + 6 = 10; 10 + 6 = 16).
• Numerators at even positions (2nd, 4th): 20, 14. This sequence decreases by 6 (20 - 6 = 14).
• To find the 6th term's numerator (an even position), we continue the second pattern: 14 - 6 = 8.

Therefore, the numerator for the missing term is 8.

Denominator Progression

Now, let's analyze the sequence of denominators: 23, G, 17, M, 11, ?

Convert letters to their numerical positions: 23, 7, 17, 13, 11, ?

We observe two interleaved patterns here as well:

• Denominators at odd positions (1st, 3rd, 5th): 23, 17, 11. This sequence decreases by 6 each time (23 - 6 = 17; 17 - 6 = 11).
• Denominators at even positions (2nd, 4th): G (7), M (13). This sequence increases by 6 (7 + 6 = 13).
• To find the 6th term's denominator (an even position), we continue the second pattern: 13 + 6 = 19.

The 19th letter of the alphabet is S. So, the denominator for the missing term is S.

Determining the Missing Term

Combining the calculated numerator (8) and denominator (S), the missing term in the series is $\displaystyle \frac{8}{\text{S}}$.