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Tier 10.7 h to studyMedium confidenceEasyabout 3.5 questions2.7% of paper

L3 - Number and letter series

1. Why this topic matters here

Expected load: 3.51 questions, 2.7% of a ~130-question paper (logical section, tier 1, confidence Medium).

That figure is a proportional allocation of the section's budget by evidence weight, not a count of anything observed, and the 130-question structure itself is [LIKELY], not published. It ranks at tier 1 because of its estimated marks per study hour (4.01, against a paper-wide mean of 2.52). No question on this topic was observed on any L&T paper found. See section 10.

2. Exactly what gets asked

Sub-pattern How it appears Roughly how often
Number series, constant difference 4, 9, 14, 19, __ Most common single form
Number series, growing difference 2, 6, 12, 20, __ Very common
Number series, multiply / divide ratio 3, 6, 12, 24, __ Common
Multiply-then-add mixed rule 5, 11, 23, 47, __ Common
Square / cube / prime base 1, 4, 9, 16, __ Common
Interleaved two-series odd and even positions follow different rules Occasional
Letter series, forward shift B, E, H, K, __ Common
Letter pair series, opposed shift AZ, BY, CX, __ Occasional
Alphanumeric mixed series A1, C3, E5, __ Occasional
Wrong-term identification one term of a series is incorrect Occasional
Missing middle term blank sits in the middle, not the end Occasional

3. Concept notes

3.1 Letter position values

Every letter has a fixed position 1-26 from the front and 1-26 from the back.

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.

Position from the back = 27 minus position from the front. Example: C is 3rd from the front and 27-3 = 24th from the back.

Do not count on your fingers. Anchor with EJOTY: E=5, J=10, O=15, T=20, Y=25. Example: to find R, go back two from T=20, so R=18.

3.2 The first-difference method

Write the gaps between consecutive terms. If the gaps are constant, the series is arithmetic. Example: 7, 11, 15, 19 has gaps 4, 4, 4.

If gaps are not constant, write the gaps of the gaps (the second difference). A constant second difference means a quadratic series. Example: 2, 5, 10, 17 has first gaps 3, 5, 7 and second gaps 2, 2.

The next term is always the last term plus the next gap. Example: 2, 5, 10, 17, __ → next gap 9 → 26.

3.3 Alternating and second-order differences

When gaps alternate in sign or size, read odd gaps and even gaps separately. Example: 10, 20, 15, 30, 25 has gaps +10, -5, +15, -5 → next is +20 → 45.

3.4 Multiply, divide, and mixed rules

Test each term against the one before it:

  • Constant ratio: term × k. Example: 5, 15, 45, 135 (k = 3).
  • Multiply then add a counter: term × 2 + 1, then × 2 + 2, then × 2 + 3. Example: 3, 7, 16, 35 (3×2+1=7, 7×2+2=16, 16×2+3=35).
  • Multiply then subtract a constant: term × 2 − 1. Example: 4, 7, 13, 25.
  • Divide then add: term ÷ 2 + 1. Example: 64, 33, 17.5 — rare, exam series usually stay integral.

3.5 Square, cube, prime and Fibonacci bases

Base Series Rule
Squares 1, 4, 9, 16, 25 n²
Squares ±1 2, 5, 10, 17, 26 n² + 1
Squares ±k 3, 8, 15, 24, 35 n² − 1
Cubes 1, 8, 27, 64, 125 n³
Primes 2, 3, 5, 7, 11, 13 primes only
Fibonacci 1, 1, 2, 3, 5, 8, 13 term = sum of previous two
Product form 2, 6, 12, 20, 30 n(n+1)

Recognise n(n+1) instantly: 2, 6, 12, 20, 30, 42 is the sequence of products of consecutive integers. It is the same as 1×2, 2×3, 3×4, 4×5, 5×6, 6×7.

3.6 Interleaved series

Long series with 7 or more terms are often two series shuffled together. Split into positions 1, 3, 5, 7 and positions 2, 4, 6, 8 and solve each separately. Example: 3, 100, 6, 90, 12, 80, 24 → odd positions double (3, 6, 12, 24), even positions drop by 10 (100, 90, 80).

3.7 Letter series rules

Apply the same difference method to letter positions. Example: B(2), E(5), H(8), K(11) has gap +3 each time, so the next is N(14).

For letter pairs, treat each letter as its own series. Example: AZ, BY, CX, DW → first letters A, B, C, D advance by +1; second letters Z, Y, X, W retreat by −1. Next is EV.

For a pair moving in opposite directions, note that the two positions always add to 27. Example: A+Z = 1+26 = 27, B+Y = 2+25 = 27. This is a fast cross-check.

3.8 Wrong-term identification

Find the rule using the first four terms, then test every later term. The first term that breaks the rule is the answer. Do not hunt for a rule that fits all seven terms — in a wrong-term question no such rule exists by construction.

3.9 The 30-second decision tree

  1. Write first differences. Constant? Answer.
  2. Not constant — write second differences. Constant? Answer.
  3. Ratio between consecutive terms roughly constant? Answer by multiplication.
  4. Ratio near 2 with a small offset? Test ×2 ± 1, ×2 ± 2, ×2 ± 3.
  5. Terms look like 1, 4, 9, 16 or 1, 8, 27, 64? Answer by square or cube.
  6. More than 7 terms? Split odd and even positions.
  7. Letters? Convert to numbers first, then run steps 1-6.

4. Must-memorise block

Reverse position rule: front position + back position = 27.

EJOTY anchors: E=5, J=10, O=15, T=20, Y=25.

Mid-alphabet anchor: M=13, N=14.

Squares 1-15 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Cubes 1-10 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Primes below 50 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Fibonacci 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
n(n+1) series 2, 6, 12, 20, 30, 42, 56, 72, 90, 110
n²+1 series 2, 5, 10, 17, 26, 37, 50, 65
n²−1 series 0, 3, 8, 15, 24, 35, 48, 63

Fast arithmetic pairings used in wrong-term questions: ×2+1 (3→7→15→31→63), ×2−1 (4→7→13→25→49→97), ×3+1 (2→7→22→67).

5. Worked examples

Example 1. Find the next term: 2, 6, 12, 20, 30, __

First differences: 4, 6, 8, 10. These rise by 2 each time, so the next difference is 12. 30 + 12 = 42. Cross-check: the terms are n(n+1), and 6×7 = 42. The slow method — testing a quadratic formula by hand — costs 40 seconds and gains nothing.

Example 2. Find the next term: 5, 11, 23, 47, 95, __

Each term is roughly double the previous. Test ×2+1: 5×2+1 = 11, 11×2+1 = 23, 23×2+1 = 47, 47×2+1 = 95. Rule confirmed. 95×2+1 = 191. The slow method of computing differences (6, 12, 24, 48) works too, but you then need a second step to see the doubling; the ratio test answers in one line.

Example 3. Find the next term: AZ, BY, CX, DW, __

Split the pair. First letters: A(1), B(2), C(3), D(4) → +1 → E(5). Second letters: Z(26), Y(25), X(24), W(23) → −1 → V(22). Check: 5 + 22 = 27, the reverse-pair rule holds. Answer EV.

Example 4. Find the next term: 3, 7, 16, 35, 74, __

Ratio is just over 2. Test ×2+k with k rising: 3×2+1 = 7, 7×2+2 = 16, 16×2+3 = 35, 35×2+4 = 74. Rule confirmed. 74×2+5 = 153. The difference method gives 4, 9, 19, 39 which is not obviously patterned — ratio-first is strictly faster here.

Example 5. Find the wrong term: 5, 8, 13, 20, 31, 40

Differences: 3, 5, 7, 11, 9. The first three gaps rise by 2 (3, 5, 7), so the pattern is odd numbers 3, 5, 7, 9, 11. The fourth gap should be 9, giving 20 + 9 = 29, not 31. Then 29 + 11 = 40 matches the given last term. The wrong term is 31.

6. Traps and gotchas

Trap Why it catches people How to avoid it
Stopping at the first difference A series with gaps 4, 6, 8 looks irregular until you see the gaps rise by 2 Always compute the second difference before giving up on a series
Assuming doubling when the rule is ×2+k 5, 11, 23, 47 looks like pure doubling at a glance Compute ×2+k for the actual first term and check k against later terms
Counting letters on fingers Costs 20-30 seconds per question and introduces off-by-one errors Use EJOTY anchors and add or subtract from them
Forgetting the reverse alphabet A series running Z, X, V, T looks negative when it is just −2 Convert to numbers immediately; Z=26, so Z, X, V, T is 26, 24, 22, 20
Ignoring interleaving on long series Seven-term series are usually two series, not one complex rule Split odd and even positions when the term count is 7 or more
In wrong-term questions, hunting for a rule that fits everything No such rule exists; the question is built so one term breaks it Derive the rule from the first four terms only, then test forward
Treating a missing middle term as a missing last term 2, 5, __, 17, 26 needs the gap pattern, and the gaps are 3, 5, 7, 9 Write all known gaps first, then fill the blank
Assuming a series must use one operation throughout Mixed rules like ×2+1 then +3 then ×2+1 are standard Test the operation pair, not a single operation

7. Practice questions

1. Find the next term: 4, 9, 14, 19, 24, __ a) 27 b) 28 c) 30 d) 29

2. Find the next term: 3, 6, 12, 24, 48, __ a) 72 b) 96 c) 108 d) 84

3. Find the next term: B, E, H, K, __ a) M b) O c) N d) L

4. Find the next term: 1, 4, 9, 16, 25, __ a) 30 b) 36 c) 49 d) 42

5. Find the next term: 2, 3, 5, 7, 11, __ a) 15 b) 12 c) 13 d) 17

6. Find the next term: 7, 14, 28, 56, __ a) 84 b) 98 c) 120 d) 112

7. Find the next term: AZ, CX, EV, GT, __ a) HS b) IQ c) JR d) IR

8. Find the next term: 2, 5, 10, 17, 26, __ a) 35 b) 36 c) 37 d) 39

9. Find the next term: 4, 7, 13, 25, 49, __ a) 95 b) 97 c) 96 d) 99

10. Find the next term: 1, 8, 27, 64, __ a) 125 b) 100 c) 121 d) 144

11. Find the next term: 6, 11, 21, 41, 81, __ a) 161 b) 162 c) 160 d) 151

12. Find the wrong term: 2, 6, 12, 20, 30, 42, 58 a) 58 b) 42 c) 30 d) 20

ANSWER KEY

  1. d — Constant difference of 5: 24 + 5 = 29.
  2. b — Constant ratio ×2: 48 × 2 = 96.
  3. c — Positions 2, 5, 8, 11 rise by 3, so the next is 14 = N.
  4. b — Consecutive squares: 1² to 5², next is 6² = 36.
  5. c — Consecutive primes: 2, 3, 5, 7, 11, next is 13.
  6. d — Constant ratio ×2: 56 × 2 = 112.
  7. d — First letters A, C, E, G advance by 2 → I(9); second letters Z, X, V, T retreat by 2 → R(18); 9 + 18 = 27 confirms the pairing, so IR.
  8. c — Terms are n² + 1: 1+1, 4+1, 9+1, 16+1, 25+1, next is 36+1 = 37.
  9. b — Rule ×2 − 1 throughout: 4→7, 7→13, 13→25, 25→49, next 49×2−1 = 97.
  10. a — Consecutive cubes: 1³, 2³, 3³, 4³, next is 5³ = 125.
  11. a — Rule ×2 − 1 throughout: 6→11, 11→21, 21→41, 41→81, next 81×2−1 = 161.
  12. a — Terms are n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42, 7×8 = 56, so 58 is wrong and should be 56.

8. Resources

  • Number Series - Logical Reasoning Questions and Answers — https://www.indiabix.com/logical-reasoning/number-series/ — MCQ set with options, answers and explanations (verified).
  • Letter and Symbol Series - Logical Reasoning Questions and Answers — https://www.indiabix.com/logical-reasoning/letter-and-symbol-series/ — MCQ set with options, answers and explanations (verified).
  • Aptitude Questions and Answers — https://www.geeksforgeeks.org/quantitative-aptitude/ — index of question sets - open a sub-topic for the actual questions.
  • Aptitude Questions and Answers — https://www.geeksforgeeks.org/quantitative-aptitude/ — index of question sets - open a sub-topic for the actual questions.
  • Fibonacci sequence - Wikipedia — https://en.wikipedia.org/wiki/Fibonacci_sequence — reference article.

9. Self-check

  1. Can you state the position of any letter A-Z without counting from A?
  2. Can you give the back-alphabet position of any letter using the 27-minus rule in under two seconds?
  3. Can you write the squares 1-15 and cubes 1-10 from memory without hesitating?
  4. Do you write second differences automatically when first differences are irregular?
  5. Do you split any series with 7 or more terms into odd and even positions before trying anything else?
  6. In a wrong-term question, do you derive the rule from the first four terms only and then test forward?

If all six are yes, stop studying this topic.

10. Sources

Evidence status: confidence Medium. High needs a recent observed question, and none exists for any topic.

Syllabus lists only [INFERRED]. No observed question and no first-hand mention. This topic appears in aggregator syllabus pages and search summaries, some of which could not be separated from LTTS or LTIMindtree material. Treat it as a reasonable guess about what a paper like this contains.

Not evidence of the current paper. The official notice names only "analytical, verbal, and numerical ability" and "domain-specific knowledge"; nothing in it lists topics. See research/05-source-audit.md.