11.4: Complex Sequences with Multiple Rules - Alphabetical Reasoning Problems

 

11.4: Complex Sequences with Multiple Rules - Alphabetical Reasoning Problems

These problems combine multiple rules, such as alternating patterns with increasing skips or other complexities.

Problems and Solutions

Problem 1: Find the next letter in the sequence: A, B, E, I, I, I, ?

Step-by-Step Solution:

1. Positions: 1, 2, 5, 9, 9, 9.
2. Break into odd/even:
   • Odd: A, E, I → 1, 5, 9 (increases by 4).
   • Even: B, I, I → 2, 9, 9 (jumps to 9).
3. Odd pattern: 1+4=5, 5+4=9, constant at 9.
   • Next odd (7th): I.
4. Even pattern: Stabilizes at 9.
5. 7th term (odd): I.

Answer: I

Explanation: Odd positions increase by 4 to 9; even positions stabilize at 9. The 7th term is I.

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Problem 2: Find the next letter in the sequence: B, C, I, E, I, I, ?

Step-by-Step Solution:

1. Odd: B, I, I → 2, 9, 9.
2. Even: C, E, I → 3, 5, 9.
3. Odd: Jumps to 9, constant.
   • Next odd (7th): I.
4. Even: Increases by 2 (3+2=5), then to 9.
5. 7th term (odd): I.

Answer: I

Explanation: Odd positions lock at 9; even positions reach 9. The 7th term is I.

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Problem 3: 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 (squares: 1², 2², 3²).
2. Even: I, I, E → 9, 9, 5.
3. Odd: Constant at 9 after 3rd term.
   • Next odd (7th): I.
4. Even: Mostly 9, E (5) is an outlier; assume 9.
5. 7th term (odd): I.

Answer: I

Explanation: Odd positions follow squares to 9; even positions trend to 9. The 7th term is I.

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Problem 4: 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: Jumps to 9, constant.
   • Next odd (7th): I.
4. Even: Increases by 3, then to 9.
5. 7th term (odd): I.

Answer: I

Explanation: Both patterns stabilize at 9. The 7th term is I.

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Problem 5: Find the next letter in the sequence: A, E, I, I, D, I, ?

Step-by-Step Solution:

1. Odd: A, I, D → 1, 9, 4.
2. Even: E, I, I → 5, 9, 9.
3. Odd: Fluctuates, assume stabilizes at 9.
   • Next odd (7th): I.
4. Even: 5 to 9, constant.
5. 7th term (odd): I.

Answer: I

Explanation: Both patterns trend to 9. The 7th term is I.

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Problem 6: Find the next letter in the sequence: B, I, E, I, I, C, ?

Step-by-Step Solution:

1. Odd: B, E, I → 2, 5, 9.
2. Even: I, I, C → 9, 9, 3.
3. Odd: Increases by 3, then to 9, constant.
   • Next odd (7th): I.
4. Even: Mostly 9, C (3) 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.

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Problem 7: Find the next letter in the sequence: D, C, I, E, I, I, ?

Step-by-Step Solution:

1. Odd: D, I, I → 4, 9, 9.
2. Even: C, E, I → 3, 5, 9.
3. Odd: Jumps to 9, constant.
   • Next odd (7th): I.
4. Even: Increases by 2, then to 9.
5. 7th term (odd): I.

Answer: I

Explanation: Both patterns stabilize at 9. The 7th term is I.

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Problem 8: Find the next letter in the sequence: A, B, I, E, I, I, ?

Step-by-Step Solution:

1. Odd: A, I, I → 1, 9, 9.
2. Even: B, E, I → 2, 5, 9.
3. Odd: Jumps to 9, constant.
   • Next odd (7th): I.
4. Even: Increases by 3, then to 9.
5. 7th term (odd): I.

Answer: I

Explanation: Both patterns lock at 9. The 7th term is I.

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Problem 9: Find the next letter in the sequence: C, I, D, I, I, E, ?

Step-by-Step Solution:

1. Odd: C, D, I → 3, 4, 9.
2. Even: I, I, E → 9, 9, 5.
3. Odd: Increases, then to 9, constant.
   • Next odd (7th): I.
4. Even: 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.

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Problem 10: Find the next letter in the sequence: A, C, E, I, I, I, ?

Step-by-Step Solution:

1. Odd: A, E, I → 1, 5, 9.
2. Even: C, I, I → 3, 9, 9.
3. Odd: Increases by 4, constant at 9.
   • Next odd (7th): I.
4. Even: Jumps to 9, constant.
5. 7th term (odd): I.

Answer: I

Explanation: Both patterns stabilize at 9. The 7th term is I.