Series Pattern Analysis

The question asks us to identify the missing term in the given letter series: NR, UQ, TX, AW, ?. To find the missing term, we need to decode the pattern governing the sequence.

We can break down the series into pairs and analyze the progression of the first and second letters independently.

First Letter Pattern Analysis

Let's examine the first letter of each pair: N, U, T, A.

We assign numerical positions to these letters based on their place in the English alphabet:

• N = 14
• U = 21
• T = 20
• A = 1

Now, we calculate the difference between consecutive first letters:

• From N (14) to U (21): $21 - 14 = +7$
• From U (21) to T (20): $20 - 21 = -1$
• From T (20) to A (1): Considering the alphabet wraps around (Z is 26, A is 1, or 27), the difference is $27 - 20 = +7$.

The observed pattern for the first letters is an alternating sequence of adding 7 and subtracting 1: +7, -1, +7.

To find the next letter, we apply the next operation in the sequence, which is -1.

Applying this to A (position 1): $1 - 1 = 0$. When we wrap around the alphabet (where Z is the 26th letter), the position 0 corresponds to Z.

So, the next first letter in the series is Z.

Second Letter Pattern Analysis

Next, let's analyze the second letter of each pair: R, Q, X, W.

We assign their numerical positions:

• R = 18
• Q = 17
• X = 24
• W = 23

Now, let's calculate the difference between consecutive second letters:

• From R (18) to Q (17): $17 - 18 = -1$
• From Q (17) to X (24): $24 - 17 = +7$
• From X (24) to W (23): $23 - 24 = -1$

The pattern for the second letters is also an alternating sequence: -1, +7, -1.

Following this pattern, the next operation should be +7.

Applying this to W (position 23): $23 + 7 = 30$.

To find the corresponding letter, we wrap around the 26-letter alphabet. The position is $30 \pmod{26}$. This equals 4 ($30 - 26 = 4$).

The 4^th letter of the alphabet is D.

So, the next second letter in the series is D.

Missing Term Identification

Combining the results from our analysis:

• The next first letter is Z.
• The next second letter is D.

Therefore, the missing term that completes the series NR, UQ, TX, AW, ? is ZD.