Finding the Missing Term in the Series

The question asks us to identify the missing term in the given series: J2AZ, M4BY, L6CX, O8DW, ?, Q12FU. This is a letter-number series problem where each term follows a specific pattern. We need to analyze the pattern for the letters and the numbers separately.

Analyzing the First Letter Pattern

Let's look at the first letter of each term:

J, M, L, O, ?, Q

Let's consider their positions in the English alphabet (A=1, B=2, ..., Z=26):

J(10), M(13), L(12), O(15), ?, Q(17)

Observing the sequence of positions: 10, 13, 12, 15, ?, 17. This pattern isn't a simple arithmetic progression. Let's look at alternate terms:

• Sequence 1 (1st, 3rd, 5th terms): J(10), L(12), ?
• Sequence 2 (2nd, 4th, 6th terms): M(13), O(15), Q(17)

In Sequence 1:

J(10) → L(12): $\text{12} - \text{10} = +\text{2}$

So, the next term in this alternate sequence should be L(12) + 2 = 14. The 14th letter is N.

In Sequence 2:

M(13) → O(15): $\text{15} - \text{13} = +\text{2}$

O(15) → Q(17): $\text{17} - \text{15} = +\text{2}$

This confirms that the pattern for the first letter follows two interleaved sequences, each increasing by 2 positions in the alphabet.

Thus, the first letter of the missing term is N.

Analyzing the Number Pattern

Now, let's examine the number in each term:

2, 4, 6, 8, ?, 12

Let's find the difference between consecutive numbers:

• 4 - 2 = 2
• 6 - 4 = 2
• 8 - 6 = 2

The pattern for the number is a consistent increase of 2. So, the next number should be 8 + 2 = 10.

Thus, the number in the missing term is 10.

Analyzing the Third Letter Pattern

Let's look at the third letter of each term:

A, B, C, D, ?, F

Observing the sequence:

• A → B: +1 (next letter)
• B → C: +1 (next letter)
• C → D: +1 (next letter)

The pattern for the third letter is a consistent increase by 1 position in the alphabet. So, the next letter should be D + 1 = E.

Thus, the third letter of the missing term is E.

Analyzing the Fourth Letter Pattern

Finally, let's examine the fourth letter of each term:

Z, Y, X, W, ?, U

Observing the sequence:

• Z → Y: -1 (previous letter)
• Y → X: -1 (previous letter)
• X → W: -1 (previous letter)

The pattern for the fourth letter is a consistent decrease by 1 position in the alphabet. So, the next letter should be W - 1 = V.

Thus, the fourth letter of the missing term is V.

Combining the Patterns

Based on our analysis:

• First letter: N
• Number: 10
• Third letter: E
• Fourth letter: V

Combining these gives the missing term: N10EV.

Checking the Options

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

1. N9EV
2. P10GH
3. N10EV
4. P10EV

Our missing term N10EV matches option 3.

The patterns observed are:

• 1st Letter: Alternate series +2 (J → L → N) and +2 (M → O → Q)
• Number: +2 in each step (2 → 4 → 6 → 8 → 10 → 12)
• 3rd Letter: +1 in each step (A → B → C → D → E → F)
• 4th Letter: -1 in each step (Z → Y → X → W → V → U)

Thus, the missing term is N10EV.

Revision Table: Series Patterns

Additional Information: Logical Reasoning Series

Logical reasoning series questions test your ability to identify patterns in sequences of numbers, letters, or alphanumeric combinations. These patterns can be arithmetic, geometric, based on differences, alternate series, or follow specific rules like alphabet positions or skipping.

Key strategies for solving series problems:

• Look for simple arithmetic progressions (addition, subtraction).
• Check for multiplication or division patterns.
• Analyze the differences between consecutive terms.
• Examine alternate terms for separate patterns.
• For letter series, consider their positions in the alphabet.
• For alphanumeric series, analyze the letter part and the number part independently.
• Combine different patterns if necessary.
• Verify the identified pattern across all given terms before determining the missing one.

Solving these questions requires careful observation and systematic analysis of each component of the series.