Letter Series Analysis: F, R, ?, Z, E, H, M
This solution explains how to find the missing letter in the given alphabetical series: F, R, ?, Z, E, H, M.
Step 1: Mapping Letters to Numbers
To understand the pattern, we first assign numerical positions to each letter based on its place in the English alphabet (A=1, B=2, ..., Z=26).
| Letter | Alphabetical Position |
|---|---|
| F | 6 |
| R | 18 |
| ? | ? |
| Z | 26 |
| E | 5 |
| H | 8 |
| M | 13 |
The series represented numerically is: 6, 18, ?, 26, 5, 8, 13.
Step 2: Finding the Pattern in the Series
Let's examine the difference between consecutive known letters. Remember that the alphabet wraps around (after Z comes A).
Calculate the differences between the numerical positions:
- From F (6) to R (18): The difference is $18 - 6 = +12$.
- From Z (26) to E (5): To move from Z to E, we count 5 steps forward (Z $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ D $\rightarrow$ E). The difference is +5. Mathematically, this can be calculated as $(26 - 26) + 5 = +5$, or more generally $(5 - 26) \pmod{26} = -21 \pmod{26} = +5$.
- From E (5) to H (8): The difference is $8 - 5 = +3$.
- From H (8) to M (13): The difference is $13 - 8 = +5$.
The sequence of differences we've found is: +12, (gap), (gap), +5, +3, +5.
Observe the pattern in the last three steps: +5, +3, +5. This strongly suggests an alternating addition pattern of 5 and 3.
Step 3: Determining the Missing Letter
Assuming the alternating pattern (+5, +3) begins after the initial +12 jump, the complete sequence of operations should be: +12, +5, +3, +5, +3, +5.
Let's apply this pattern step-by-step to find the missing letter:
- Starting letter: F (position 6).
- First operation: Add 12. $6 + 12 = 18$. This corresponds to R.
- Second operation: Add 5. $18 + 5 = 23$. The 23rd letter of the alphabet is W. This is our potential missing letter.
- Third operation: Add 3. $23 + 3 = 26$. The 26th letter is Z. This matches the series.
- Fourth operation: Add 5. $26 + 5 = 31$. Wrapping around the alphabet: $31 \pmod{26} = 5$. The 5th letter is E. This matches the series.
- Fifth operation: Add 3. $5 + 3 = 8$. The 8th letter is H. This matches the series.
- Sixth operation: Add 5. $8 + 5 = 13$. The 13th letter is M. This matches the series.
The numerical series derived using this pattern is: 6, 18, 23, 26, 5, 8, 13.
Step 4: Conclusion
The identified pattern (+12, +5, +3, +5, +3, +5) successfully generates the known letters in the series. The number 23, which follows the pattern, corresponds to the letter W.
Therefore, the letter that replaces the question mark (?) is W.
The complete series is: F, R, W, Z, E, H, M.
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Important Questions from Alphabet Series
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_ a _ b _ abaa _ bab _ abbSelect the combination of letters that when sequentially placed in the blanks of the given series will complete the series.
Q _ P _ M _ A _ T _ Q A _ T M
In the series _b_a_ba_b_abab_aab;
fill in the six blanks ( _ ) using one of the following given four choices such that the series follows a specific order.
