Finding the Pattern in Letter Series

The question asks us to identify the pattern in the given letter series and determine the next letter. The series is E, F, I, N, U, ?.

To solve letter series questions, we often look at the alphabetical positions of the letters or the difference in positions between consecutive letters. Let's list the positions of the given letters in the English alphabet:

• E is the 5th letter.
• F is the 6th letter.
• I is the 9th letter.
• N is the 14th letter.
• U is the 21st letter.

Now, let's find the difference in positions between consecutive letters:

• From E to F: Position of F - Position of E = \(6 - 5 = 1\). The difference is 1.
• From F to I: Position of I - Position of F = \(9 - 6 = 3\). The difference is 3.
• From I to N: Position of N - Position of I = \(14 - 9 = 5\). The difference is 5.
• From N to U: Position of U - Position of N = \(21 - 14 = 7\). The difference is 7.

The differences in positions between consecutive letters are 1, 3, 5, 7. This sequence of differences consists of consecutive odd numbers.

Following this pattern, the next difference should be the next odd number after 7, which is 9.

To find the position of the next letter in the series, we add this next difference (9) to the position of the last letter in the series (U), which is 21.

Position of next letter = Position of U + Next difference

Position of next letter = \(21 + 9 = 30\)

Since there are only 26 letters in the English alphabet (A-Z), a position greater than 26 usually indicates a wrap-around from Z back to A. To find the letter for position 30, we can subtract 26 (the total number of letters).

Effective position = \(30 - 26 = 4\)

The letter at the 4th position in the English alphabet is D.

Therefore, the next letter in the series E, F, I, N, U, ? is D.

Let's check the given options:

• Option 1: A (1st letter)
• Option 2: N (14th letter)
• Option 3: Z (26th letter)
• Option 4: D (4th letter)

Our calculated letter D matches Option 4.

Revision Table: Alphabetical Positions

Additional Information: Letter Series Patterns

Letter series questions in reasoning ability tests can follow various patterns. Understanding common types helps in quickly identifying the rule. Some common patterns include:

• Alphabetical Position Difference: The pattern is based on the difference between the positions of consecutive letters, which can be a constant, an arithmetic progression (like 1, 3, 5, 7 in this question), a geometric progression, squares, cubes, etc.
• Skip Letters: A fixed number of letters are skipped between consecutive terms.
• Reversal: The series might involve writing the alphabet in reverse order or using positions from the end of the alphabet.
• Combination of Patterns: Sometimes, two different series might be interleaved, or the pattern might combine position difference with another rule.
• Vowel/Consonant Pattern: The series might alternate between vowels and consonants or follow a specific sequence related to them.
• Specific Word/Phrase: Less common, but the letters might be the initials of words in a sequence (e.g., days of the week, months of the year).

Practicing different types of letter series helps in recognizing the underlying logic more quickly during exams.