Solving the Letter-Number Sequence: E1, H2, K6, N24, ______

This question asks us to find the missing term in a sequence that combines letters and numbers. To solve this, we need to analyze the pattern in the letters and the pattern in the numbers separately.

Analyzing the Letter Pattern in the Sequence E1, H2, K6, N24

Let's look at the letters in the given sequence: E, H, K, N.

We can find the position of each letter in the English alphabet:

• E is the 5th letter.
• H is the 8th letter.
• K is the 11th letter.
• N is the 14th letter.

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

• From E (5th) to H (8th): $8 - 5 = 3$ positions
• From H (8th) to K (11th): $11 - 8 = 3$ positions
• From K (11th) to N (14th): $14 - 11 = 3$ positions

The pattern for the letters is that each subsequent letter is 3 positions after the previous one in the alphabet. Following this pattern, the next letter should be 3 positions after N (14th).

The 14th letter + 3 positions = 17th letter.

The 17th letter of the alphabet is Q.

Analyzing the Number Pattern in the Sequence E1, H2, K6, N24

Next, let's look at the numbers associated with each letter: 1, 2, 6, 24.

Let's find the relationship between consecutive numbers:

• From 1 to 2: Multiply by 2 ($1 \times 2 = 2$)
• From 2 to 6: Multiply by 3 ($2 \times 3 = 6$)
• From 6 to 24: Multiply by 4 ($6 \times 4 = 24$)

The pattern for the numbers is that each subsequent number is obtained by multiplying the previous number by consecutive integers, starting from 2. The multipliers are 2, 3, 4, and so on.

Following this pattern, the next number should be obtained by multiplying the last number (24) by the next integer in the sequence of multipliers, which is 5.

Next number = $24 \times 5 = 120$.

Determining the Missing Term

We found that the next letter in the sequence is Q and the next number is 120.

Combining these, the missing term is Q120.

Why Other Options are Incorrect

• Q72: The letter Q is correct, but the number 72 does not follow the multiplication pattern ($24 \times 5 = 120$, not 72).
• P120: The number 120 is correct, but the letter P is the 16th letter, which does not follow the +3 letter pattern (N is 14th, $14+3=17$, which is Q).
• Q720: The letter Q is correct, but the number 720 does not follow the multiplication pattern ($24 \times 5 = 120$, not 720).

Only Q120 follows both the letter pattern (+3 to alphabetical position) and the number pattern (multiply by consecutive integers starting from 2).

Revision Table: Sequence Analysis Summary

Additional Information on Solving Letter-Number Sequences

Letter-number sequences are common in reasoning tests. They often follow independent patterns for the letters and the numbers. Here are some tips for solving them:

• Analyze Letters: Look at the alphabetical position (A=1, B=2, etc.) and see if there is a constant difference, increasing/decreasing difference, or a pattern based on vowels/consonants or specific groups of letters.
• Analyze Numbers: Look for arithmetic progressions (adding/subtracting a constant), geometric progressions (multiplying/dividing by a constant), squares, cubes, factorials, prime numbers, or patterns involving consecutive integers in multiplication or division.
• Check for Interaction: Sometimes, the number pattern might depend on the letter's position or vice versa, but usually, they are independent.
• Break it Down: Solve the letter part and the number part separately before combining them.
• List Positions: Writing out the alphabetical positions can make the letter pattern easier to spot.