Analyzing the Alphabetical Series

The provided series is: CHR, HMW, MRB, RWG, ?

The task is to identify the pattern based on the English alphabet order and determine the missing term represented by the question mark (?).

Deconstructing the Pattern

We will analyze the pattern for each letter position (1st, 2nd, 3rd) across the terms in the series.

First Letter Progression

The first letters of the terms are C, H, M, R.

Assigning numerical values based on alphabetical position (A=1, B=2, ...):

• C = 3
• H = 8
• M = 13
• R = 18

Calculating the difference between consecutive letters:

• $8 - 3 = 5$
• $13 - 8 = 5$
• $18 - 13 = 5$

The pattern is adding 5 to the position of the previous letter. The next first letter will be at position $18 + 5 = 23$. The 23rd letter of the alphabet is W.

Second Letter Progression

The second letters of the terms are H, M, R, W.

Assigning numerical values:

• H = 8
• M = 13
• R = 18
• W = 23

Calculating the difference:

• $13 - 8 = 5$
• $18 - 13 = 5$
• $23 - 18 = 5$

This position also follows the pattern of adding 5. The next second letter will be at position $23 + 5 = 28$. Since the alphabet has 26 letters, we wrap around ($28 \pmod{26}$). The resulting position is $28 - 26 = 2$. The 2nd letter of the alphabet is B.

Third Letter Progression

The third letters of the terms are R, W, B, G.

Assigning numerical values:

• R = 18
• W = 23
• B = 2
• G = 7

Calculating the difference, including wrap-around:

• $23 - 18 = 5$ (W)
• $23 + 5 = 28$. $28 \pmod{26} = 2$ (B)
• $2 + 5 = 7$ (G)

This position also follows the pattern of adding 5 with wrap-around. The next third letter will be at position $7 + 5 = 12$. The 12th letter of the alphabet is L.

Concluding the Series

Combining the next letters determined for each position:

• First letter: W
• Second letter: B
• Third letter: L

Therefore, the missing term in the series is WBL.