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Double / Alternate Letter Series

Introduction

In a Double / Alternate Letter Series, two (or more) alphabetic sub-sequences are interleaved. Each sub-sequence follows its own rule (for example: forward by +1, backward by -1, or jumps of +n), and the overall series alternates between them.

These questions test your ability to split the sequence into its component patterns and solve each independently before recombining the result.

Pattern: Double / Alternate Letter Series

Pattern

The key idea: split the sequence into two (or more) alternating sub-series and identify the progression in each.

Formula:
Treat letters as positions: A = 1, B = 2, …, Z = 26 and apply standard arithmetic progressions to each sub-series:
n-th term of sub-series = a1 + (k - 1) × d
where a1 is the first term of that sub-series, d is the common difference, and k counts positions inside the sub-series (not the full series).

Step-by-Step Example

Question

Find the next letter in the series: A, Z, B, Y, C, X, D, ?

Solution

  1. Step 1: Split into sub-series

    Odd-position letters (1st, 3rd, 5th, 7th): A, B, C, D.
    Even-position letters (2nd, 4th, 6th, 8th): Z, Y, X, ?.

  2. Step 2: Identify the pattern in each sub-series

    Odd sub-series: A(1) → B(2) → C(3) → D(4) → increases by +1 each step.
    Even sub-series: Z(26) → Y(25) → X(24) → decreases by -1 each step.

  3. Step 3: Apply the rule to find the missing term

    Next even-position letter after X(24) = 24 - 1 = 23 → Letter = W.

  4. Final Answer:

    W

  5. Quick Check:

    Odd positions: A, B, C, D (↑+1). Even positions: Z, Y, X, W (↓-1) ✅

Quick Variations

1. Forward / Forward but different gaps: A, C, B, D, C, E → two forward sequences with different step sizes.

2. Forward / Backward: A, Z, C, X, E, V → odd positions +2, even positions -2.

3. Letter-number alternation combined: A, 1, C, 3, E, 5 → letters follow +2, numbers follow +2.

4. More than two sub-series (three-way alternation): A, M, Z, B, N, Y, C, O, X → split into three sequences.

Trick to Always Use

  • Step 1 → Convert letters to numeric positions (A=1 … Z=26).
  • Step 2 → Separate odd and even positions (or however many interleaved sequences) into groups.
  • Step 3 → Find the common difference for each group individually.
  • Step 4 → Calculate the next term for the appropriate sub-series and convert back to a letter.

Summary

Summary

In Double / Alternate Letter Series problems:

  • Always split the sequence into its alternating sub-series first.
  • Work out the progression (common difference) inside each sub-series.
  • Apply the correct sub-series rule to the missing position.
  • Convert between letters and numeric positions where it simplifies arithmetic.

Example to remember: A, Z, B, Y, C, X, D, W → Odd: +1 (A→D), Even: -1 (Z→W)

Practice

(1/5)
1. Find the next letter in the series: L, A, M, B, N, C, O, ?
easy
A. P
B. Q
C. R
D. D

Solution

  1. Step 1: Split into sub-series

    Odd positions: L, M, N, O → positions 12,13,14,15. Even positions: A, B, C, ? → positions 1,2,3,...

  2. Step 2: Identify patterns

    Odd sub-series increases by +1 (L→M→N→O). Even sub-series increases by +1 (A→B→C→D).

  3. Step 3: Apply rule

    Next (even position) after C(3) is 3 + 1 = 4 → Letter = D.

  4. Final Answer:

    D → Option D

  5. Quick Check:

    Odd: 12,13,14,15 → L,M,N,O. Even: 1,2,3,4 → A,B,C,D ✅
Hint: Split into odd/even positions and continue each sub-series separately.
Common Mistakes: Mixing up odd/even positions or applying the same rule to both without checking.
2. Find the next letter: B, G, C, H, D, I, E, ?
easy
A. J
B. F
C. K
D. L

Solution

  1. Step 1: Separate sub-series

    Odd positions: B, C, D, E → positions 2,3,4,5. Even positions: G, H, I, ? → positions 7,8,9,...

  2. Step 2: Identify patterns

    Odd sub-series: +1 each step (B→C→D→E). Even sub-series: +1 each step (G→H→I→J).

  3. Step 3: Apply rule

    Next (even position) after I(9) is 9 + 1 = 10 → Letter = J.

  4. Final Answer:

    J → Option A

  5. Quick Check:

    Odd: B,C,D,E (↑+1). Even: G,H,I,J (↑+1) ✅
Hint: If both sub-series move forward by the same step, expect identical increments.
Common Mistakes: Mis-indexing positions and choosing the wrong sub-series.
3. Find the next letter in the series: A, M, B, N, C, O, ?
easy
A. E
B. D
C. F
D. G

Solution

  1. Step 1: Split into sub-series

    Odd positions: A, B, C → 1,2,3. Even positions: M, N, O → 13,14,15.

  2. Step 2: Identify patterns

    Odd sub-series increases by +1 (A→B→C). Even sub-series increases by +1 (M→N→O).

  3. Step 3: Apply rule

    Next term is odd-position after C → C(3) + 1 = 4 → Letter = D.

  4. Final Answer:

    D → Option B

  5. Quick Check:

    Odd: A,B,C,D (↑+1). Even: M,N,O (↑+1) ✅
Hint: Work on each interleaved sequence independently before recombining.
Common Mistakes: Confusing which letters belong to which sub-series.
4. Find the next letter: P, Z, Q, Y, R, X, S, ?
medium
A. T
B. V
C. W
D. U

Solution

  1. Step 1: Split the sequence

    Odd positions: P, Q, R, S → 16,17,18,19. Even positions: Z, Y, X, ? → 26,25,24,...

  2. Step 2: Identify patterns

    Odd sub-series increases by +1 (P→Q→R→S). Even sub-series decreases by -1 (Z→Y→X→W).

  3. Step 3: Apply rule

    Next (even position) after X(24) is 24 - 1 = 23 → Letter = W.

  4. Final Answer:

    W → Option C

  5. Quick Check:

    Odd: P,Q,R,S (↑+1). Even: Z,Y,X,W (↓-1) ✅
Hint: When sub-series move in opposite directions, splitting is the fastest way to see both rules.
Common Mistakes: Assuming both sub-series progress the same way.
5. Find the next letter: A, Z, C, X, E, V, G, ?
medium
A. T
B. U
C. S
D. R

Solution

  1. Step 1: Separate sub-series

    Odd positions: A, C, E, G → numeric positions 1, 3, 5, 7 (increments of +2). Even positions: Z, X, V, ? → numeric positions 26, 24, 22, ... (decrements of -2).

  2. Step 2: Identify rules

    Odd sub-series increases by +2 each step (A→C→E→G). Even sub-series decreases by -2 each step (Z→X→V→T).

  3. Step 3: Apply the rule

    Next (even position) after V (22) is 22 - 2 = 20 → letter = T.

  4. Final Answer:

    T → Option A

  5. Quick Check:

    Odd: A,C,E,G (positions 1,3,5,7 → +2). Even: Z,X,V,T (26,24,22,20 → -2) ✅
Hint: When gaps are larger than 1, try ±2 or ±3 in the sub-series.
Common Mistakes: Assuming ±1 steps when the series actually jumps by more than one letter.

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