Understanding the Letter Series Pattern

The question asks us to find the missing term in the given letter series: FH, LN, RT, ?.

To solve this, we need to analyze the pattern within each pair of letters and the pattern between consecutive pairs of letters.

Pattern within each pair:

Let's look at the position of the letters in the English alphabet (A=1, B=2, ..., Z=26).

• FH: F is the 6th letter, H is the 8th letter. The difference in position is \(\text{H} - \text{F} = 8 - 6 = 2\).
• LN: L is the 12th letter, N is the 14th letter. The difference in position is \(\text{N} - \text{L} = 14 - 12 = 2\).
• RT: R is the 18th letter, T is the 20th letter. The difference in position is \(\text{T} - \text{R} = 20 - 18 = 2\).

It is clear that within each pair, the second letter is always 2 positions ahead of the first letter in the alphabet.

Pattern between consecutive pairs (using the first letter of each pair):

Now, let's look at the first letter of each term in the series: F, L, R, ?

• F to L: F is the 6th letter, L is the 12th letter. The difference is \(\text{L} - \text{F} = 12 - 6 = 6\).
• L to R: L is the 12th letter, R is the 18th letter. The difference is \(\text{R} - \text{L} = 18 - 12 = 6\).

It appears that the first letter of each subsequent term is 6 positions ahead of the first letter of the previous term.

Finding the Missing Term

Using the pattern identified:

1. The first letter of the missing term should be 6 positions ahead of R. R is the 18th letter. The 18th letter + 6 positions = 24th letter. The 24th letter is X.
2. The second letter of the missing term should be 2 positions ahead of the first letter (X). X is the 24th letter. The 24th letter + 2 positions = 26th letter. The 26th letter is Z.

Therefore, the missing term is XZ.

Verifying with Options

Let's check our answer XZ against the given options.

• Option 1: XY. X is 24, Y is 25. Difference is 1. Does not follow the +2 pattern within the pair.
• Option 2: XZ. X is 24, Z is 26. Difference is 2. Follows the +2 pattern within the pair. The first letter X is 6 positions after R (18+6=24). Follows the +6 pattern between pairs.
• Option 3: ZX. Z is 26, X is 24. Difference is -2. Does not follow the +2 pattern within the pair.
• Option 4: WY. W is 23, Y is 25. Difference is 2. Follows the +2 pattern within the pair. However, the first letter W (23) is not 6 positions after R (18).

Option XZ correctly fits both identified patterns.

Summary of Patterns

Based on the analysis, the missing term that completes the series FH, LN, RT, ? is XZ.

Revision Table: Letter Series

Additional Information: Solving Alphabet Series

Alphabet series questions are common in reasoning sections of exams. They can involve single letters, pairs of letters, or groups of letters. The patterns can be based on:

• Position in Alphabet: Simple addition, subtraction, multiplication, or division of letter positions.
• Skip Letters: Skipping a fixed number of letters between terms.
• Vowels/Consonants: Patterns based on the sequence of vowels or consonants.
• Reverse Alphabetical Order: Patterns moving backward through the alphabet.
• Combination of Patterns: Multiple rules applied simultaneously, as seen in this problem (one rule within the pair, another between pairs).

To solve these types of questions effectively, it is helpful to:

• Write down the alphabet with their corresponding positions (1-26).
• Look for patterns in the differences between consecutive terms (or letters within terms).
• Consider different types of patterns (arithmetic, skipped letters, etc.).
• Test the identified pattern on all given terms in the series.
• Apply the pattern to find the missing term.
• Verify the answer with the options.