Alphabet Positions and Letter Series

What you will learn

You will follow a rule through an ordered list of English letters. You will use alphabet positions, changing gaps, alternating term positions, two-letter blocks and explicitly stated cycles. The earlier analogy lesson already introduced A=1 through Z=26. Keep its habit of checking every supplied example; here you must check every step of a sequence.

A term is one entry in the sequence. Its term position tells you where it appears: first, second, third, and so on. Its alphabet position tells you where the letter sits in A–Z. In M, C, R, the first term is M, but M's alphabet position is 13. Mixing these two kinds of position causes avoidable errors.

A finite list can be continued in many ways if no rule is specified. Every assessed series in this module declares a rule family or a finite menu of permitted rules. Your answer is justified within that stated domain; it is not proof that no other formula could fit the same finite list.

1 A short starting check

These four unscored prompts locate useful revision. They do not lock the course or set an official pass mark.

1. The declared rule is “double the input, then add 1”. Do both 3→7 and 5→11 fit? Yes: 2×3+1=7 and 2×5+1=11. “Double only” fails both pairs. Keep the exact rule and test all evidence.
2. Recall alphabet position and the count strictly between two letters using the next short example.
3. Evaluate (8−2)÷3×4. Brackets give 6÷3×4; division and multiplication have equal priority, so 2×4=8. Revise the signed-arithmetic/BODMAS lesson if needed.
4. Recall 6²=36 and 24÷6=4. These small powers and exact divisions will support number series later; a full square-root lesson is not required.

Worked example

Use the English alphabet A=1 through Z=26.

Letter: K; find its left/right positions and the number of letters strictly between D and K.

Answer: K: 11 from the left, 16 from the right; 6 letters strictly between D and K.

Right position is 27−11; the between-count is 11−4−1.

Watch the mistake: Do not call the position difference 7 the between-count.

Use this lookup when you need it; memorising a shortcut is not the learning goal:

A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13

N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26

For a letter at left position p, its right position is 27−p. For two different letters at positions p and q, the number strictly between is |p−q|−1. The absolute difference means the nonnegative distance between their positions. Do not use the between-count as the size of a shift.

2 A fixed shift

First translate the letters to numbers. If the question says the same shift is used at each step, subtract one position from the next and check that the difference stays fixed. “Move three places” means three moves; it does not mean skip three letters and then land on the following one.

Worked example

Each step uses the same forward shift. Do not wrap past Z.

B, E, H, K, ?

Answer: N

Positions 2, 5, 8, 11 have a difference of +3 throughout; 14 is N.

Watch the mistake: Count moves, not letters skipped.

An internal blank needs two checks. The step from the previous known term into the blank and the step out of the blank to the next known term must both obey the rule. A letter that fits only one side is not enough.

3 When the gaps change regularly

Some questions specify a rule for the gaps rather than one fixed letter shift. Write a position row and then a gap row. Decide what changes in the gap row before extending the letter row. Never add the last gap automatically when the question says the gaps are growing.

Worked example

Each forward gap is one larger than the preceding gap; no wraparound.

A, C, F, J, O, ?

Pause and complete the working row

Letters: A, C, F, J, O, ?

Positions: 1, 3, 6, 10, 15, □

Gaps: +2, +3, +4, +5, □

Fill the new gap first, then the next position, then the letter. Do this before reading the answer below.

Answer: U

Positions 1, 3, 6, 10, 15 give gaps 2, 3, 4, 5. Next gap 6 gives 21=U.

Watch the mistake: Repeating +5 would ignore the stated growth in gaps.

The completed gap is +6 and the completed position is 21. The row explains U; it is more informative than merely recognising the answer letter.

4 Two sequences taking turns

If the question declares separate rules for odd and even term positions, number the terms first. Positions 1,3,5,… form one row; positions 2,4,6,… form the other. “Odd positions” does not mean letters with odd alphabet values. Keep the two row rules separate, even when their values happen to meet.

Worked example

Odd and even term positions form separate constant-shift sequences; no wraparound.

C, V, F, S, I, P, L, ?

Pause and separate the positions

The blank is term 8. The odd positions are 1,3,5,7 and the even positions are 2,4,6,8.

Even-position letters: V, S, □, ?

Their alphabet positions: 22, 19, □, ?

Complete the known entry, find this row's step, then fill its final entry. Write the intermediate entries yourself before reading the worked answer below.

Answer: M

Odd-position letters C,F,I,L move +3; even-position letters V,S,P,M move −3.

Watch the mistake: Odd/even refers to positions 1,2,…, not odd/even alphabet values.

In the even row the step is −3, so 16−3=13=M. The missing term belongs to this row because its term position is 8. The odd row C,F,I,L also fits its own +3 rule throughout.

5 Blocks have columns

A term can contain more than one letter. In a two-letter block, track the first letters down one column and the second letters down another. Do not compare only the alphabet gap inside a single block when the stated rule concerns changes from block to block.

Worked example

In each two-letter block, the first column has a fixed forward shift and the second a fixed backward shift; no wraparound.

AZ, CX, EV, ?

Answer: GT

First column A,C,E,G is +2; second Z,X,V,T is −2.

Watch the mistake: Do not reverse the target block or apply the first-column shift to both columns.

Check the complete answer block. Getting one column right is not sufficient, and reversing the letters creates a different block.

6 Crossing the end of the alphabet

Do not assume a cycle. In a non-cyclic question, a proposed rule that demands a position beyond 26 or below 1 does not fit the stated domain. In a cyclic question, the stem must explicitly permit returning to A after Z, or moving back to Z before A. The move Z→A is one step, not zero.

Worked example

Advance three English-alphabet positions each time, returning to A after Z.

V, Y, B, E, ?

Answer: H

22→25→2→5→8; Y→B crosses Z and A.

Watch the mistake: The cycle is permission in this question, not a universal assumption.

For small shifts, counting the boundary moves is enough. You do not need modular-arithmetic notation. Preserve the same English letters in Hindi questions; the language of the explanation does not change the alphabet being used.

7 A solving routine you can check

1. Read the permitted rule family and the cycle condition
2. Number term positions separately from alphabet positions
3. Build the appropriate row: adjacent gaps, odd/even subsequences or block columns
4. Check the rule against every supplied term
5. Fill the blank and check again, including both sides of an internal blank

Independent practice

Try all five before reading the key. Each is an original untimed learning question: one mark for a correct answer, zero for an incorrect or unattempted answer, with no negative marking or pass cutoff. These local practice settings do not describe the RRB exam's marking rules.

1. The English-letter sequence D, H, ?, P, T uses the same forward position shift at every step, with no wraparound. Which letter fills the blank?

A. K B. L C. M D. N

2. In B, E, I, N, ?, each forward English-alphabet gap is one larger than the preceding gap. There is no wraparound. Find the next letter.

A. R B. S C. U D. T

3. In D, Y, H, V, L, S, ?, P, the odd term positions and the even term positions each form a separate constant-shift English-letter sequence. No wraparound occurs. Find the missing letter at position 7.

A. P B. O C. R D. N

4. For BY, EU, HQ, ?, the first letter of each block follows one fixed forward shift and the second follows one fixed backward shift in the English alphabet. No wraparound occurs. Which block comes next?

A. LM B. KO C. KM D. MK

5. Starting with N, move four English-alphabet positions forward each time and return to A after Z: N, R, V, Z, ?. What is the next letter?

A. C B. D C. E D. F

Explained key

1. B — L

D(4)→H(8) is +4. Filling L(12) gives 4,8,12,16,20, with +4 at every step. Both H→L and L→P fit. A gives gaps +3 and +5 around K; C gives +5 and +3 around M; D gives +6 and +2 around N. None preserves the fixed shift.

2. D — T

The positions are 2,5,9,14, with gaps +3,+4,+5. The next gap is +6, so 14+6=20=T. A uses +4, going back to an earlier gap. B repeats +5. C uses +7 and skips the required +6 gap.

3. A — P

Odd positions 1,3,5,7 contain D(4),H(8),L(12),P(16): their step is +4. Even positions 2,4,6,8 contain Y(25),V(22),S(19),P(16): their step is −3. A repeated P at positions 7 and 8 is allowed because the subsequences have different rules. B gives only +3 from L; C gives +6; D gives +2. Each breaks the odd-position +4 rule.

4. C — KM

Read columns: B(2),E(5),H(8),K(11) gives +3; Y(25),U(21),Q(17),M(13) gives −4. Thus KM preserves both rules. A uses L rather than K in the first column. B moves the second column back only two places to O. D reverses the required block.

5. B — D

The positions are 14→18→22→26, all +4. From Z count four moves: A(1), B(2), C(3), D(4). Hence D is correct. A stops after three moves; C makes five; D makes six. The option label D is not the letter D: option B contains the required letter.

Source and scope

RRB CEN 09/2025, §14.1, printed p.28, names alphabetical and number series, coding and decoding, and mathematical operations. The topic list is illustrative, not exhaustive. University of Cambridge NRICH supports the fixed-shift and explicit-cycle coding idea. We consistently use A=1 through Z=26. All explanations, examples and questions here are original teaching material. The selected subtypes and question counts are learning choices, not official topic weightage. These are not previous-year questions or a full reasoning course.

Analogy

Imagine 26 numbered lockers labelled A to Z. A letter series tells you how to move between locker numbers. Two alternating series are like two people taking turns: record each person’s moves separately. A two-letter block tracks two locker positions at once. Only a question that explicitly turns the row into a loop lets a move beyond Z return to A. The locker picture helps track positions; the declared rule still decides the moves.

Quick reference

• Term position: entry number in the sequence; alphabet position: A=1,…,Z=26
• Right position = 27 − left position
• For distinct letters, letters strictly between = absolute position difference − 1
• Fixed shift: check every consecutive difference
• Changing gaps: extend the gap row before the letter row
• Alternation: split positions 1,3,5,… and 2,4,6,…
• Blocks: test every column, keeping letter order
• Wraparound applies only when stated; count Z→A as one forward move
• Every assessed sequence uses an explicit family/menu; check the target within it