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Zorluk: Çok zorNumber and Alphabet Series

Determine the underlying double-pattern rule governing the alphanumeric series below and find the term that logically completes it.

Cevap:In the sequence Z12,X25,U52,Q107,L218,…Z12, X25, U52, Q107, L218, \dots, the missing term that should replace the blank is 【F441】.

Cevap

The missing term in the sequence is F441.
The sequence consists of two distinct intertwined logic rules: the letter component decreases positional value by progressive increments (-2, -3, -4, -5, -6), turning L (12th letter) into F (6th letter). The numerical component follows the recurrence formula Tn=2×Tn−1+(n−1)T_{n} = 2 \times T_{n-1} + (n-1), where the additive constant increases by 1 each step (+1, +2, +3, +4, +5), yielding 218×2+5=441218 \times 2 + 5 = 441. Combining both gives F441.

Adım Adım Çözüm

1
Analyze the alphabetical component by converting letters to their corresponding numerical positions in the alphabet (A=1, B=2, ..., Z=26).
The letter sequence corresponds to positions: Z (26), X (24), U (21), Q (17), L (12).
Tracking positional values helps identify decremental positional shifts.
2
Determine the difference pattern between consecutive letter positions.
26 - 2 = 24 (X); 24 - 3 = 21 (U); 21 - 4 = 17 (Q); 17 - 5 = 12 (L). The positional shift decreases by consecutive integers (-2, -3, -4, -5).
The next shift must be -6, giving position 12 - 6 = 6, which corresponds to the letter F.
3
Analyze the numerical component of the series: 12, 25, 52, 107, 218.
12 × 2 + 1 = 25; 25 × 2 + 2 = 52; 52 × 2 + 3 = 107; 107 × 2 + 4 = 218.
The numerical pattern multiplies the preceding term by 2 and adds an incrementing integer starting from +1.
4
Calculate the next numerical term using the derived recurrence rule.
218 × 2 + 5 = 436 + 5 = 441.
Applying the next multiplier and additive step (×2 + 5) yields 441.
5
Combine the letter and number components.
The completed missing term is F441.
Combining the 6th letter 'F' and calculated number '441' forms the full missing term.

Anahtar Kavram

Interleaved positional decrements combined with linear multiplicative-additive recurrence relation.
Tahmini Süre:2m 0s
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Konular

Number and Alphabet Series

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