11.2: Alternating Sequences (Interleaved Patterns) - Alphabetical Reasoning Problems

 

11.2: Alternating Sequences (Interleaved Patterns) - Alphabetical Reasoning Problems
These problems involve sequences where odd and even positions (or other interleaved subsets) follow distinct patterns. You must separate the sub-sequences to identify the rules.
Problems and Solutions
Problem 1: Find the next letter in the sequence: A, B, C, E, I, I, ?
Step-by-Step Solution:
  1. Separate into odd and even positions:
    • Odd: 1st, 3rd, 5th (A, C, I) → Positions: 1, 3, 9.
    • Even: 2nd, 4th, 6th (B, E, I) → Positions: 2, 5, 9.
  2. Odd positions (1, 3, 9):
    • Pattern: 1×3=3, 3×3=9 (multiplicative or squares: 1², 3²).
    • Next odd position (7th term): Continues at 9 (I).
  3. Even positions (2, 5, 9):
    • Pattern: Increases by 3 (2+3=5), then by 4 (5+4=9), or stabilizes at 9.
    • Next even position (if sequence continues): Likely 9 (I).
  4. Since the 7th term is an odd position, use the odd pattern: I.
Answer: I
Explanation: The sequence alternates between two patterns. Odd positions follow a multiplicative or square pattern (1, 3, 9), and even positions approach 9. The 7th term, being odd, is I.
Problem 2: Find the next letter in the sequence: B, C, D, I, I, I, ?
Step-by-Step Solution:
  1. Odd: B, D, I (1st, 3rd, 5th) → 2, 4, 9.
  2. Even: C, I, I (2nd, 4th, 6th) → 3, 9, 9.
  3. Odd pattern: 2×2=4, then jumps to 9 and stays at 9.
    • Next odd (7th): I (9).
  4. Even pattern: Jumps from 3 to 9 and stays at 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Odd positions double then stabilize at 9; even positions jump to 9. The 7th term is odd, so I.
Problem 3: Find the next letter in the sequence: A, E, C, I, I, I, ?
Step-by-Step Solution:
  1. Odd: A, C, I → 1, 3, 9.
  2. Even: E, I, I → 5, 9, 9.
  3. Odd pattern: 1×3=3, 3×3=9, stabilizes at 9.
    • Next odd (7th): I.
  4. Even pattern: 5 to 9, then constant at 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Odd positions follow a multiplicative pattern to 9; even positions stabilize at 9. The 7th term is I.
Problem 4: Find the next letter in the sequence: B, I, D, E, I, I, ?
Step-by-Step Solution:
  1. Odd: B, D, I → 2, 4, 9.
  2. Even: I, E, I → 9, 5, 9.
  3. Odd pattern: 2×2=4, then to 9, constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Fluctuates but stabilizes at 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Both subsequences converge to 9. The 7th term is I.
Problem 5: Find the next letter in the sequence: A, C, I, E, I, I, ?
Step-by-Step Solution:
  1. Odd: A, I, I → 1, 9, 9.
  2. Even: C, E, I → 3, 5, 9.
  3. Odd pattern: Jumps from 1 to 9, constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Increases by 2 (3+2=5), then to 9, constant at 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Both patterns stabilize at 9. The 7th term is I.
Problem 6: Find the next letter in the sequence: C, B, I, E, I, I, ?
Step-by-Step Solution:
  1. Odd: C, I, I → 3, 9, 9.
  2. Even: B, E, I → 2, 5, 9.
  3. Odd pattern: 3 to 9, constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Increases by 3 (2+3=5), then to 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Both subsequences lock at 9. The 7th term is I.
Problem 7: Find the next letter in the sequence: A, I, D, I, I, E, ?
Step-by-Step Solution:
  1. Odd: A, D, I → 1, 4, 9.
  2. Even: I, I, E → 9, 9, 5.
  3. Odd pattern: Squares (1², 2², 3²), constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Stabilizes at 9, but E (5) is an anomaly; assume returns to 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Odd positions follow squares to 9; even positions converge to 9. The 7th term is I.
Problem 8: Find the next letter in the sequence: B, E, I, I, D, I, ?
Step-by-Step Solution:
  1. Odd: B, I, D → 2, 9, 4.
  2. Even: E, I, I → 5, 9, 9.
  3. Odd pattern: Fluctuates but seems to stabilize (assume 9 based on context).
    • Next odd (7th): I.
  4. Even pattern: 5 to 9, constant at 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Both patterns trend toward 9. The 7th term is I.
Problem 9: Find the next letter in the sequence: A, I, C, I, I, E, ?
Step-by-Step Solution:
  1. Odd: A, C, I → 1, 3, 9.
  2. Even: I, I, E → 9, 9, 5.
  3. Odd pattern: 1×3=3, 3×3=9, constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Mostly 9, E (5) is an outlier; assume 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Odd positions reach 9; even positions trend to 9. The 7th term is I.
Problem 10: Find the next letter in the sequence: D, B, I, E, I, I, ?
Step-by-Step Solution:
  1. Odd: D, I, I → 4, 9, 9.
  2. Even: B, E, I → 2, 5, 9.
  3. Odd pattern: 4 to 9, constant at 9.
    • Next odd (7th): I.
  4. Even pattern: Increases by 3 (2+3=5), then to 9.
  5. 7th term (odd): I.
Answer: I
Explanation: Both subsequences stabilize at 9. The 7th term is I.

Comments

Post a Comment

|

Blog Archive

Show more