Letter Series Completion: M, O, R, V, ?

The task is to identify the pattern in the given sequence of letters (M, O, R, V) and determine the next letter that logically follows.

Determining Letter Positions

To understand the pattern, we first find the numerical position of each letter in the English alphabet:

• M is the 13^th letter.
• O is the 15^th letter.
• R is the 18^th letter.
• V is the 22^nd letter.

Finding the Pattern in Differences

Next, we calculate the difference between the positions of consecutive letters in the series:

• The gap between O (15) and M (13) is $15 - 13 = 2$.
• The gap between R (18) and O (15) is $18 - 15 = 3$.
• The gap between V (22) and R (18) is $22 - 18 = 4$.

We observe a clear pattern in these differences: they are increasing by 1 each time (+2, +3, +4).

Predicting the Next Letter

Based on the observed pattern (+2, +3, +4), the next difference in the sequence should be 5.

To find the position of the missing letter, we add this difference (5) to the position of the last known letter (V, which is 22):

Position of the next letter = $22 + 5 = 27$.

The English alphabet consists of 26 letters. When the position count exceeds 26, it wraps around to the beginning. Therefore, the 27th position corresponds to the 1st letter of the alphabet.

Mathematically, this can be represented as $27 \pmod{26} = 1$.

The 1st letter of the alphabet is A.

Conclusion

Thus, the next letter in the series M, O, R, V is A.