Select the letter cluster that will replace the question mark (?) in the following series. RBT, OER, KIP, FNN, ZTL, ?
SAJ
Analyzing the Letter Series Pattern
The question asks us to identify the next letter cluster in the given series: RBT, OER, KIP, FNN, ZTL, ? We need to find a logical pattern governing the sequence of these three-letter clusters.
To solve this, we will examine the pattern for each letter position (first, second, and third) separately across the series.
Decoding the First Letter Progression
Let's look at the first letters of each cluster: R, O, K, F, Z.
We find their positions in the English alphabet:
- R is the 18th letter (\(R_{18}\))
- O is the 15th letter (\(O_{15}\))
- K is the 11th letter (\(K_{11}\))
- F is the 6th letter (\(F_{6}\))
- Z is the 26th letter (\(Z_{26}\))
Now, let's find the difference between the positions of consecutive letters:
- \(O_{15} - R_{18} = 15 - 18 = -3\)
- \(K_{11} - O_{15} = 11 - 15 = -4\)
- \(F_{6} - K_{11} = 6 - 11 = -5\)
- \(Z_{26} - F_{6}\): To go from F (6) back to Z (26), we subtract 6 positions (\(6 - 6 = 0\), which wraps around to the 26th position). So, the difference is \(-6\).
The pattern for the differences is \(-3, -4, -5, -6\). This is a sequence where we subtract consecutive integers starting from 3.
Following this pattern, the next difference should be \(-7\). We apply this to the last letter Z (\(Z_{26}\)):
- \(26 - 7 = 19\).
The 19th letter of the alphabet is S. So, the first letter of the next cluster is S.
Analyzing the Second Letter Sequence
Next, let's examine the second letters: B, E, I, N, T.
Their positions in the alphabet are:
- B is the 2nd letter (\(B_{2}\))
- E is the 5th letter (\(E_{5}\))
- I is the 9th letter (\(I_{9}\))
- N is the 14th letter (\(N_{14}\))
- T is the 20th letter (\(T_{20}\))
Let's find the difference between the positions of consecutive letters:
- \(E_{5} - B_{2} = 5 - 2 = +3\)
- \(I_{9} - E_{5} = 9 - 5 = +4\)
- \(N_{14} - I_{9} = 14 - 9 = +5\)
- \(T_{20} - N_{14} = 20 - 14 = +6\)
The pattern observed here is \(+3, +4, +5, +6\). This is a sequence where we add consecutive integers starting from 3.
The next step in this pattern should be adding 7. We apply this to the last letter T (\(T_{20}\)):
- \(20 + 7 = 27\).
Since there are only 26 letters, the 27th position means we wrap around the alphabet. The 27th position corresponds to the 1st letter, which is A. (\(27 \pmod{26} = 1\)). So, the second letter of the next cluster is A.
Establishing the Third Letter Pattern
Finally, let's analyze the third letters: T, R, P, N, L.
Their positions in the alphabet are:
- T is the 20th letter (\(T_{20}\))
- R is the 18th letter (\(R_{18}\))
- P is the 16th letter (\(P_{16}\))
- N is the 14th letter (\(N_{14}\))
- L is the 12th letter (\(L_{12}\))
Let's calculate the difference between the positions of consecutive letters:
- \(R_{18} - T_{20} = 18 - 20 = -2\)
- \(P_{16} - R_{18} = 16 - 18 = -2\)
- \(N_{14} - P_{16} = 14 - 16 = -2\)
- \(L_{12} - N_{14} = 12 - 14 = -2\)
The pattern here is consistent: subtract 2 from the position of the previous letter.
To find the next letter, we subtract 2 from the position of L (\(L_{12}\)):
- \(12 - 2 = 10\).
The 10th letter of the alphabet is J. So, the third letter of the next cluster is J.
Synthesizing the Final Letter Cluster
By analyzing each position, we found the letters for the next cluster:
- First letter: S
- Second letter: A
- Third letter: J
Combining these, the next letter cluster in the series is SAJ.
Comparing this result with the given options:
- RAJ
- SBJ
- SAJ
- SAK
Our calculated cluster, SAJ, matches option 3.
Conclusion: The Correct Option
The pattern analysis reveals that the next letter cluster in the series RBT, OER, KIP, FNN, ZTL is SAJ.
Therefore, the correct option is 3.
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Important Questions from Alphabet Series
A series is given with some letters missing. Choose the correct alternative from the given ones that will complete the series:
BR __ __ NB __ O __ NBA series is given with some letters missing. Choose the set of letters which when sequentially placed shall complete it .
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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.
G _ C T _ X _ T G X _ T _ X C T G _ C T
Select 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
