In the sequence of single letters A, E, I, M, which of the following letters should come next to continue the pattern?

Introduction / Context:
This is a straightforward letter series question involving single letters: A, E, I, M, followed by a missing term. To solve it, we should look for a consistent step pattern in alphabet positions, often a fixed increment in numeric value. Because these letters seem evenly spaced, converting them to their positions can quickly reveal the underlying arithmetic pattern.

Given Data / Assumptions:

• Given series: A, E, I, M, ?
• Alphabet positions: A 1, E 5, I 9, M 13.
• We must choose the next letter from P, Q, R, O, S.

Concept / Approach:
The efficient method here is to treat each letter as a number and examine the differences between successive terms. If the increments are consistent, we can add the same increment to the last term to find the next one. This type of arithmetic sequence on alphabet positions is extremely common in reasoning sections of competitive exams.

Step-by-Step Solution:
Step 1: Write down the numeric positions: A is 1, E is 5, I is 9, and M is 13. Step 2: Calculate the differences: from 1 to 5 is +4, from 5 to 9 is +4, and from 9 to 13 is +4. Step 3: The increment is consistently +4 between each pair of letters. Step 4: Apply the same increment to M. M is 13, so adding 4 gives 17. Step 5: The 17th letter of the English alphabet is Q. Step 6: Therefore, the next letter in the series must be Q.

Verification / Alternative check:
We can write the full extended series in numeric form: 1, 5, 9, 13, 17, which is clearly an arithmetic progression with common difference 4. Mapping 17 back to its letter form gives Q. Checking all options, only Q has this position. Hence, Q is the unique answer that fits the pattern of constant incremental steps.

Why Other Options Are Wrong:
P is the 16th letter, which would result from an increment of 3 rather than 4 from 13, breaking the consistent difference.
R is the 18th letter, which would require an increment of 5 from 13.
O is the 15th letter, which again fails to maintain the plus four pattern.
S is the 19th letter, giving an increment of 6, not 4. Thus none of these match the clear arithmetic progression of the series.

Common Pitfalls:
One common mistake is to look at the letters as vowels and expect some irregular pattern of vowels. While A, E, and I are vowels, M is not, which shows that the pattern is numeric rather than based solely on vowel order. Converting letters to positions removes this confusion and reveals the simple numeric rule driving the series.

Final Answer:
The next letter in the sequence is Q.