5.4: Completing or Correcting a Pattern

 5.4: Completing or Correcting a Pattern

This type involves finding a missing letter or correcting a sequence to maintain a pattern.

Problem 1

Question: The sequence A, C, E, ?, I follows a pattern. What is the missing letter?

Solution Process:

• Sequence: A, C, E, ?, I.
• Positional values: A=1, C=3, E=5, ?=?, I=9.
• Pattern: Positions 1, 3, 5, ?, 9 (odd numbers: 1, 3, 5, 7, 9).
• Missing position: 7th letter = G.

Solution: G

Detailed Explanation:

• The sequence corresponds to odd-numbered positions in the alphabet.
• The 4th term should be the 7th letter (G), fitting A (1), C (3), E (5), G (7), I (9).
• This tests completing a positional pattern.

Problem 2

Question: The sequence X, Y, X, Y, ? follows a pattern. What is the missing letter?

Solution Process:

• Sequence: X, Y, X, Y, ?.
• Pattern: Alternates X, Y (period = 2).
• Positions: 1=X (odd), 2=Y (even), 3=X (odd), 4=Y (even), 5=? (odd).
• 5th (odd) = X.

Solution: X

Detailed Explanation:

• The sequence alternates XY: 1=X, 2=Y, 3=X, 4=Y.
• The 5th position is odd, so it follows X.
• This tests extending an alternating pattern.

Problem 3

Question: The sequence A, B, C, ?, E follows a pattern. What is the missing letter?

Solution Process:

• Sequence: A, B, C, ?, E.
• Pattern: Consecutive letters A, B, C, D, E.
• Missing letter: 4th position = D.

Solution: D

Detailed Explanation:

• The sequence is consecutive: A (1), B (2), C (3), D (4), E (5).
• The 4th letter is D, continuing the pattern.
• This tests completing a simple alphabetical sequence.

Problem 4

Question: The sequence P, Q, P, Q, ? follows a pattern. What is the missing letter?

Solution Process:

• Sequence: P, Q, P, Q, ?.
• Pattern: Alternates P, Q.
• Positions: 1=P, 2=Q, 3=P, 4=Q, 5=? (odd).
• 5th (odd) = P.

Solution: P

Detailed Explanation:

• The sequence alternates PQ: 1=P, 2=Q, 3=P, 4=Q.
• The 5th position is odd, so it’s P.
• This tests a two-letter alternating pattern.

Problem 5

Question: The sequence A, A, B, ?, B follows a pattern. What is the missing letter?

Solution Process:

• Sequence: A, A, B, ?, B.
• Pattern: A, A, B repeats (period = 3, but check sequence).
• Positions: 1=A, 2=A, 3=B, 4=A (expected), 5=B.
• 4th = A.

Solution: A

Detailed Explanation:

• The sequence seems to follow A, A, B, but the 5th letter (B) suggests a structural pattern.
• Assuming a continuation like A, A, B, A, B, the 4th is A.
• This tests deducing a repeating pattern.

Problem 6

Question: The sequence Z, Y, X, ?, U follows a pattern. What is the missing letter?

Solution Process:

• Sequence: Z, Y, X, ?, U.
• Positional values: Z=26, Y=25, X=24, ?=?, U=21.
• Pattern: Decreasing by 1: 26, 25, 24, 23, 22, 21 (but only 5 terms).
• 4th position: 26-3 = 23 = W.

Solution: W

Detailed Explanation:

• The sequence decreases by 1: Z (26), Y (25), X (24), W (23), U (21, but 5th term).
• The 4th term is 23rd letter = W.
• This tests a descending pattern.

Problem 7

Question: The sequence A, C, ?, I, I follows a pattern. What is the missing letter?

Solution Process:

• Sequence: A, C, ?, I, I.
• Positional values: A=1, C=3, ?=?, I=9, I=9.
• Pattern: Possible positional pattern (1, 3, 5, 9, 9).
• Assume odd positions: 3rd = 5th letter = E.

Solution: E

Detailed Explanation:

• The sequence may follow odd positions up to the 3rd term: A (1), C (3), E (5), then I, I.
• The 3rd term is the 5th letter = E.
• This tests deducing a partial pattern.

Problem 8

Question: The sequence B, D, F, ?, I follows a pattern. What is the missing letter?

Solution Process:

• Sequence: B, D, F, ?, I.
• Positional values: B=2, D=4, F=6, ?=8, I=9.
• Pattern: Even positions (2, 4, 6, 8), then I (9) breaks it.
• 4th = 8th letter = H.

Solution: H

Detailed Explanation:

• The sequence B, D, F follows even positions (2, 4, 6). The 4th should be 8 (H).
• The 5th (I) may indicate a shift, but we assume continuation to H.
• This tests an even-position pattern.

Problem 9

Question: The sequence A, B, ?, D, E follows a pattern. What is the missing letter?

Solution Process:

• Sequence: A, B, ?, D, E.
• Pattern: Consecutive letters A, B, C, D, E.
• 3rd = C.

Solution: C

Detailed Explanation:

• The sequence is consecutive: A, B, C, D, E.
• The 3rd letter is C, fitting the alphabetical order.
• This tests a simple consecutive pattern.

Problem 10

Question: The sequence M, N, O, ?, Q follows a pattern. What is the missing letter?

Solution Process:

• Sequence: M, N, O, ?, Q.
• Positional values: M=13, N=14, O=15, ?=16, Q=17.
• Pattern: Consecutive positions 13, 14, 15, 16, 17.
• 4th = 16th letter = P.

Solution: P

Detailed Explanation:

• The sequence increases by 1: M (13), N (14), O (15), P (16), Q (17).
• The 4th term is P, continuing the pattern.
• This tests a consecutive positional pattern.