Letter Series Reasoning: Finding the Missing Term

The question asks us to find the next term in the given letter series: ABC, EXG, ITK, ?

To solve letter series problems, we need to identify the pattern or rule that connects the terms. Let's examine the position of each letter in the alphabet for each term in the series.

We will look at the first letter of each term, then the second letter, and finally the third letter.

Analysing the First Letters

The first letters of the terms are A, E, I, ?. Let's note their positions in the alphabet:

• A is the 1st letter.
• E is the 5th letter.
• I is the 9th letter.

Let's find the difference in positions:

• From A (1) to E (5): \(5 - 1 = 4\)
• From E (5) to I (9): \(9 - 5 = 4\)

The pattern for the first letter seems to be adding 4 to the position of the previous term's first letter. Following this pattern, the position of the first letter of the next term should be \(9 + 4 = 13\). The 13th letter of the alphabet is M.

So, the first letter of the missing term is M.

Analysing the Second Letters

The second letters of the terms are B, X, T, ?. Let's note their positions in the alphabet:

• B is the 2nd letter.
• X is the 24th letter.
• T is the 20th letter.

Let's find the difference in positions:

• From B (2) to X (24): This can be seen as \(2 - 4 = -2\). In a cyclical alphabet (A-Z wraps around), -2 is equivalent to \(26 - 2 = 24\). So, subtracting 4.
• From X (24) to T (20): \(20 - 24 = -4\). So, subtracting 4.

The pattern for the second letter seems to be subtracting 4 from the position of the previous term's second letter, wrapping around the alphabet if needed. Following this pattern, the position of the second letter of the next term should be \(20 - 4 = 16\). The 16th letter of the alphabet is P.

So, the second letter of the missing term is P.

Analysing the Third Letters

The third letters of the terms are C, G, K, ?. Let's note their positions in the alphabet:

• C is the 3rd letter.
• G is the 7th letter.
• K is the 11th letter.

Let's find the difference in positions:

• From C (3) to G (7): \(7 - 3 = 4\)
• From G (7) to K (11): \(11 - 7 = 4\)

The pattern for the third letter seems to be adding 4 to the position of the previous term's third letter. Following this pattern, the position of the third letter of the next term should be \(11 + 4 = 15\). The 15th letter of the alphabet is O.

So, the third letter of the missing term is O.

Forming the Missing Term

Combining the letters we found:

• First letter: M
• Second letter: P
• Third letter: O

The missing term is MPO.

Comparing with Options

Let's compare the derived term MPO with the given options:

1. MPO
2. NQL
3. MPL
4. NQO

The term MPO matches Option 1.

Summary of Pattern

The pattern for the series ABC, EXG, ITK, MPO is as follows:

Revision Table: Letter Series Pattern

Additional Information: Solving Letter Series Questions

Solving letter series questions requires careful observation and pattern recognition. Here are some common patterns to look for:

• Alphabetical Position: Look at the numerical position of each letter (A=1, B=2, ..., Z=26). The pattern might involve adding, subtracting, multiplying, or dividing these positions.
• Constant Difference: The difference between the positions of corresponding letters in consecutive terms might be constant.
• Increasing/Decreasing Difference: The difference might increase or decrease by a constant value (e.g., +2, +4, +6...).
• Alternating Pattern: There might be different patterns for alternate terms or for different letter positions within a term.
• Skip Letters: The pattern might involve skipping a fixed number of letters between terms or between letters within a term.
• Reverse Alphabet: Sometimes the pattern uses the reverse alphabetical order (Z=1, Y=2, ...).
• Combinations: More complex series might combine multiple rules or apply different rules to different parts of the term.

Always break down the problem into smaller parts, usually by analysing each letter position separately. Write down the letter positions to easily identify numerical patterns.