Series & Sequences
Exhaustive AISSEE Class 6 Intelligence guide for Series & Sequences. Covers 1-tier and 2-tier difference series, squares and cubes, Fibonacci rules, alternating dual series, EJOTY letter shifts, continuous letter patterns, solved models, and 10 interactive drills.
Overview & Fundamental Concept
Exhaustive AISSEE Class 6 Intelligence guide for Series & Sequences. Covers 1-tier and 2-tier difference series, squares and cubes, Fibonacci rules, alternating dual series, EJOTY letter shifts, continuous letter patterns, solved models, and 10 interactive drills.
Official Syllabus Coverage Breakdown
| Syllabus Item | Prescribed Scope | Exam Relevance & Pedagogical Objective |
|---|---|---|
| Item 5 | Number series (arithmetic differences, 2-tier difference of differences, geometric progressions, powers n² ± k, n³ ± k, prime sequences, Fibonacci, alternating interleaved series), letter series (single, double, triple letter shifts using EJOTY), alphanumeric sequences, continuous pattern repeating series, and finding the wrong term in a series. | Identify the underlying progression logic in numerical, alphabetical, and alphanumeric sequences and pinpoint the missing term or anomalous term in under 35 seconds. |
1. Single & Multi-Tier Difference Series (Arithmetic & Geometric)
- A Numerical Series is an ordered sequence of numbers governed by a definite mathematical rule or operational pattern.
- 1. Constant Arithmetic Difference Series: Each successive term increases or decreases by a fixed constant value $d$ ($T_{n+1} = T_n + d$).
• Example: $5, 11, 17, 23, 29, ?$ (Pattern: $+6$ throughout; next term $= 29 + 6 = 35$). - 2. Linearly Increasing/Decreasing Difference Series: The difference between consecutive terms is not constant, but itself increases or decreases by a regular step.
• Example: $2, 5, 10, 17, 26, ?$ (Differences: $+3, +5, +7, +9 implies$ next difference is $+11$; next term $= 26 + 11 = 37$). - 3. Two-Tier Difference Series (Difference of Differences $\Delta_1, \Delta_2$): When the first layer of differences (Tier 1: $\Delta_1$) does not show an obvious pattern, compute the second layer of differences (Tier 2: $\Delta_2$). If $\Delta_2$ is constant, the series is quadratic ($an^2 + bn + c$).
• Sequence: $3, 8, 17, 30, 47, ?$
• Tier 1 Differences: $5, 9, 13, 17$ (arithmetic sequence with common difference $+4$).
• Tier 2 Differences: $4, 4, 4$ (constant).
• Next Tier 1 difference $= 17 + 4 = 21 implies$ next term $= 47 + 21 = 68$. - 4. Geometric Progression (Multiplication / Division Series): Each term is obtained by multiplying or dividing the preceding term by a fixed ratio $r$.
• Multiplying: $3, 6, 12, 24, 48, ?$ (Pattern: $\times 2$; next term $= 48 \times 2 = 96$).
• Halving / Dividing: $640, 320, 160, 80, ?$ (Pattern: $\div 2$; next term $= 80 \div 2 = 40$). - 5. Mixed Multiplication-Addition Operations ($n \times a \pm b$): Terms grow faster than simple addition but slower than pure exponential growth.
• Example: $3, 7, 15, 31, 63, ?$ (Pattern: $\times 2 + 1$; next term $= 63 \times 2 + 1 = 127$).
• Example: $2, 5, 14, 41, 122, ?$ (Pattern: $\times 3 - 1$; next term $= 122 \times 3 - 1 = 365$).
| Series Type | Operational Formulation | Illustrative Progression | Common AISSEE Pattern | Next Term & Method |
|---|---|---|---|---|
| Constant Difference | Tₙ₊₁ = Tₙ + d | 7, 13, 19, 25, 31, ? | +6 constant step | 37 (31 + 6) |
| Increasing Difference | Tₙ₊₁ = Tₙ + (d + kn) | 4, 7, 12, 19, 28, ? | +3, +5, +7, +9 (+2 in diff) | 39 (28 + 11) |
| Two-Tier Difference | Δ₂ = constant | 2, 9, 20, 35, 54, ? | Δ₁ = 7, 11, 15, 19; Δ₂ = 4 | 77 (54 + 23) |
| Geometric Ratio | Tₙ₊₁ = Tₙ × r | 4, 12, 36, 108, ? | × 3 constant multiplier | 324 (108 × 3) |
| Mixed Multiply & Add | Tₙ₊₁ = Tₙ × a + b | 4, 9, 19, 39, 79, ? | × 2 + 1 rule | 159 (79 × 2 + 1) |
| Mixed Multiply & Subtract | Tₙ₊₁ = Tₙ × a - b | 5, 9, 17, 33, 65, ? | × 2 - 1 rule | 129 (65 × 2 - 1) |
Cadet Mnemonic • D-I-F-F-S Stepwise Protocol
D - Differences first, I - Increasing delta?, F - Factors/Multipliers?, F - Fibonacci sum?, S - Split alternating!
- 1. D: Always calculate Tier-1 differences between adjacent numbers first.
- 2. I: If differences are not constant, check if differences increase regularly (+2, +3, +4).
- 3. F: If differences explode rapidly, test for multiplication (×2, ×3) or powers.
- 4. F: If a term equals the sum of two previous terms, it is a Fibonacci variant.
- 5. S: If terms zig-zag up and down, split into two alternating interleaved series.
Exam Trick • The Constant Second-Difference Shortcut
Whenever you encounter a sequence where the differences increase by an odd-number progression ($+3, +5, +7, +9, +11$), the second difference $\Delta_2$ is always $+2$. This proves the sequence is directly related to squares: $n^2$ produces differences $3, 5, 7, 9, 11$! Immediately check if each term is $n^2 \pm k$ to write the answer in under 10 seconds.
AISSEE Trap Alert • The Prime Number Deception
Look closely at the sequence: $2, 3, 5, 7, 11, 13, ?$. Students frequently answer $15$ by thinking 'odd numbers'. But $2$ is an even number, and $9$ is conspicuously missing! This is the fundamental Prime Number Series. The next prime after $13$ is $17$, NEVER $15$!
2. Powers (Squares, Cubes), Fibonacci & Alternating Sequences
- 1. Perfect Square Series ($n^2$): Crucial squares to memorize instantly: $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100, 11^2=121, 12^2=144, 13^2=169, 14^2=196, 15^2=225, 16^2=256, 17^2=289, 18^2=324, 19^2=361, 20^2=400$.
- 2. Modified Square Series ($n^2 \pm k$ and $n^2 \pm n$):
- • $n^2 + 1$ Series: $2, 5, 10, 17, 26, 37, ?$ ($1^2+1, 2^2+1, 3^2+1, 4^2+1, 5^2+1, 6^2+1 implies 7^2+1 = 50$).
- • $n^2 - 1$ Series: $0, 3, 8, 15, 24, 35, ?$ ($1^2-1, 2^2-1, 3^2-1, 4^2-1, 5^2-1, 6^2-1 implies 7^2-1 = 48$).
- • $n^2 + n$ Series: $2, 6, 12, 20, 30, 42, ?$ ($1^2+1, 2^2+2, 3^2+3, 4^2+4, 5^2+5, 6^2+6 implies 7^2+7 = 56$).
- 3. Perfect Cube Series ($n^3$): Core cubes for AISSEE: $1^3=1, 2^3=8, 3^3=27, 4^3=64, 5^3=125, 6^3=216, 7^3=343, 8^3=512, 9^3=729, 10^3=1000$.
- 4. Modified Cube Series ($n^3 \pm k$ and $n^3 - n$):
- • $n^3 - 1$ Series: $0, 7, 26, 63, 124, 215, ?$ ($1^3-1, 2^3-1, 3^3-1, 4^3-1, 5^3-1, 6^3-1 implies 7^3-1 = 342$).
- • $n^3 + 1$ Series: $2, 9, 28, 65, 126, 217, ?$ ($1^3+1, 2^3+1, 3^3+1, 4^3+1, 5^3+1, 6^3+1 implies 7^3+1 = 344$).
- • $n^3 - n$ Series (AISSEE Classic!): $0, 6, 24, 60, 120, 210, ?$ ($1^3-1, 2^3-2, 3^3-3, 4^3-4, 5^3-5, 6^3-6 implies 7^3-7 = 336$).
- 5. Fibonacci Sequence & Addition of Preceding Terms: Each term is the exact sum of the two preceding terms: $T_n = T_{n-1} + T_{n-2}$.
• Standard Fibonacci: $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ?$ ($34 + 55 = 89$).
• Lucas Sequence / Arbitrary Starters: $2, 4, 6, 10, 16, 26, ?$ ($2+4=6; 4+6=10; 6+10=16; 10+16=26 implies 16+26 = 42$).
• 3-Term Fibonacci Sum: Each term is the sum of preceding three terms: $1, 2, 3, 6, 11, 20, 37, ?$ ($1+2+3=6; 2+3+6=11; 3+6+11=20; 6+11+20=37 implies 11+20+37 = 68$). - 6. Alternating Dual-Interleaved Series: A single composite sequence created by weaving two independent sequences together (odd positions follow Series A; even positions follow Series B).
• Example: $4, 25, 7, 20, 10, 15, 13, 10, ?, ?$
• Odd Series: $4 \xrightarrow{} 7 \xrightarrow{} 10 \xrightarrow{} 13 \xrightarrow{} 16$.
• Even Series: $25 \xrightarrow{} 20 \xrightarrow{} 15 \xrightarrow{} 10 \xrightarrow{} 5$.
| Base (n) | Square (n²) | n² - 1 | n² + 1 | Cube (n³) | n³ - 1 | n³ + 1 | n³ - n |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 2 | 1 | 0 | 2 | 0 |
| 2 | 4 | 3 | 5 | 8 | 7 | 9 | 6 |
| 3 | 9 | 8 | 10 | 27 | 26 | 28 | 24 |
| 4 | 16 | 15 | 17 | 64 | 63 | 65 | 60 |
| 5 | 25 | 24 | 26 | 125 | 124 | 126 | 120 |
| 6 | 36 | 35 | 37 | 216 | 215 | 217 | 210 |
| 7 | 49 | 48 | 50 | 343 | 342 | 344 | 336 |
| 8 | 64 | 63 | 65 | 512 | 511 | 513 | 504 |
| 9 | 81 | 80 | 82 | 729 | 728 | 730 | 720 |
| 10 | 100 | 99 | 101 | 1000 | 999 | 1001 | 990 |
Cadet Mnemonic • Z-I-G-Z-A-G Alternating Lens
When numbers oscillate up and down, never seek a single crown — split odd and even into two, and the pattern smiles at you!
- 1. Check if terms fluctuate (increase, decrease, increase, decrease).
- 2. Underline positions 1, 3, 5, 7 in pencil as Series A.
- 3. Circle positions 2, 4, 6, 8 in pencil as Series B.
- 4. Determine the rule of each independent branch separately.
Exam Trick • Spotting n³ - n Instantly
Memorize the benchmark numbers: $6, 24, 60, 120, 210, 336$. Whenever you see these exact numbers in an AISSEE exam question, do NOT waste time computing differences! They are ALWAYS $n^3 - n$ ($2^3-2, 3^3-3, 4^3-4, 5^3-5, 6^3-6, 7^3-7$). The next term after $210$ is ALWAYS $7^3 - 7 = 336$!
AISSEE Trap Alert • Fibonacci Recognition Trap
If differences keep expanding ($1, 2, 3, 5, 8, 13$), notice that the differences themselves form the Fibonacci series! Always test adding adjacent terms ($T_1 + T_2 = T_3$) before trying complex multiplications.
3. Letter Series, Alphanumeric Sequences & Continuous Patterns
- 1. Alphabet Positional Value Framework (EJOTY): Every English letter corresponds to a unique forward rank from $1$ to $26$.
• Anchor: $E=5, J=10, O=15, T=20, Y=25$.
• Finding ranks rapidly: $G = E + 2 = 7$; $M = J + 3 = 13$; $S = T - 1 = 19$; $W = T + 3 = 23$. - 2. Single Letter Progression Series: Letters shift forward or backward by a constant or increasing step.
• Example: $B, E, H, K, N, ?$ (Ranks: $2, 5, 8, 11, 14 \implies +3$ step $\implies 14 + 3 = 17 = Q$).
• Example: $Z, X, U, Q, L, ?$ (Ranks: $26, 24, 21, 17, 12 \implies -2, -3, -4, -5 \implies 12 - 6 = 6 = F$). - 3. Reverse Alphabet & Complementary Sum of 27: The sum of any letter's forward rank and reverse rank is ALWAYS 27.
• Reverse Pairs to memorize: A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N. - 4. Multi-Letter Cluster Series (Pairs and Triads): Treat each positional letter in the cluster as an independent progression.
• Example: $AB, DE, GH, JK, ?$ (1st letters: $A(1) \xrightarrow{} D(4) \xrightarrow{} G(7) \xrightarrow{} J(10) \xrightarrow{} M(13)$; 2nd letters: $B(2) \xrightarrow{} E(5) \xrightarrow{} H(8) \xrightarrow{} K(11) \xrightarrow{} N(14) \implies MN$). - 5. Alphanumeric Mixed Sequences: Formed by combining letter positions with arithmetic numbers.
• Example: $C-3, F-6, I-9, L-12, ?$ (Letter is advancing by $+3$: $C, F, I, L \implies O$; Number is multiple of 3: $3, 6, 9, 12 \implies 15$; Target $= O-15$).
• Example: $Z1A, X2D, V6G, T24J, ?$ (Letters 1: $Z, X, V, T \implies R$; Numbers: $\times 1, \times 2, \times 3, \times 4 \implies 24 \times 5 = 120$; Letters 2: $A(1), D(4), G(7), J(10) \implies M(13) \implies R120M$). - 6. Continuous Pattern Repeating Series ($a\_b\_b\_ab\_$): A string of repeating letters with missing blanks.
• Standard 4-Step Resolution Algorithm:
1. Count total characters including blanks (usually $12, 15, 16, 18,$ or $20$).
2. Factorize into equal chunks: $12 = 3 \times 4$ or $4 \times 3$; $15 = 3 \times 5$ or $5 \times 3$; $16 = 4 \times 4$; $20 = 4 \times 5$ or $5 \times 4$.
3. Divide the string into chunks and align them vertically to spot identical or cyclic repetitions.
4. Extract the letters filling the blanks in order.
| Forward Letter | Forward Rank | Reverse Pair | Reverse Rank | Sum of Ranks (Rule of 27) |
|---|---|---|---|---|
| A | 1 | Z | 26 | 1 + 26 = 27 |
| B | 2 | Y | 25 | 2 + 25 = 27 |
| C | 3 | X | 24 | 3 + 24 = 27 |
| D | 4 | W | 23 | 4 + 23 = 27 |
| E | 5 | V | 22 | 5 + 22 = 27 |
| F | 6 | U | 21 | 6 + 21 = 27 |
| G | 7 | T | 20 | 7 + 20 = 27 |
| H | 8 | S | 19 | 8 + 19 = 27 |
| I | 9 | R | 18 | 9 + 18 = 27 |
| J | 10 | Q | 17 | 10 + 17 = 27 |
| K | 11 | P | 16 | 11 + 16 = 27 |
| L | 12 | O | 15 | 12 + 15 = 27 |
| M | 13 | N | 14 | 13 + 14 = 27 |
Cadet Mnemonic • C-O-U-N-T Protocol for Continuous Letter Patterns
C - Count total slots, O - Organize equal chunks, U - Unify recurring units, N - Note down the blanks, T - Test the sound!
- 1. Count letters + blanks: e.g., 16 total slots.
- 2. 16 divides strictly into 4 groups of 4: ( _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ ).
- 3. Align each group on top of each other: compare column 1, 2, 3, 4.
- 4. Fill the corresponding characters to make all groups symmetrical.
Exam Trick • Circular Wrap-Around Letter Rule
When a pattern moves past $Z$, simply loop back to $A$: $Z + 1 = A$ (rank $27 \equiv 1$), $Z + 2 = B$ (rank $28 \equiv 2$). When moving backwards before $A$, loop back to $Z$: $A - 1 = Z$ (rank $0 \equiv 26$), $A - 2 = Y$ (rank $-1 \equiv 25$). Always use modular arithmetic ($n \pmod{26}$) for swift mental calculation!
AISSEE Trap Alert • Letter Gap vs Letter Step Trap
Do NOT confuse 'letters skipped' with 'rank difference'! If a pattern skips 2 letters ($A \to D$, skipping $B, C$), the rank difference is $+3$ ($1 + 3 = 4$). Students often mistakenly add $+2$ because 2 letters were skipped. Always write down the numeric ranks ($1 \to 4$) to prevent off-by-one errors!
4. 'Wrong Term in Series' Master Detection & Verification
- 1. What is a 'Find the Wrong Number' Problem? In these questions, an entire sequence is provided without any question mark, but exactly ONE term violates the established mathematical rule.
- 2. The Dual-Impact Signature of a Rogue Term: When one number in a series is incorrect, it corrupts TWO consecutive differences (the difference before it and the difference after it!).
- 3. The Triangulation Method to Pinpoint the Faulty Number:
- • Step 1: Compute all successive differences across the given series.
- • Step 2: Identify where the pattern breaks down. If two adjacent difference values look abnormal while all other differences follow a clean pattern, the term common to both abnormal differences is the WRONG NUMBER!
- • Step 3: Replace the suspect number with the theoretically correct value. Check if BOTH adjacent differences are instantly restored to harmony.
- • Demonstration: In $5, 10, 17, 24, 37, 50$:
- Differences are: $5, 7, 7, 13, 13$. The two anomalous differences are $7$ and $13$ around the number $24$.
- Theoretical square pattern is $n^2 + 1$: $2^2+1=5, 3^2+1=10, 4^2+1=17, 5^2+1=26, 6^2+1=37, 7^2+1=50$.
- The number $24$ should be $26$! Replacing $24$ with $26$ restores differences to $5, 7, 9, 11, 13$ perfectly!
| Given Series | Observed Differences | Anomalous Region | Underlying Correct Rule | Rogue Term & Replacement |
|---|---|---|---|---|
| 3, 5, 9, 17, 33, 64 | +2, +4, +8, +16, +31 | +16 and +31 | Powers of 2 (+2, +4, +8, +16, +32) | 64 is wrong (should be 65) |
| 2, 3, 5, 8, 12, 18, 23 | +1, +2, +3, +4, +6, +5 | +4, +6, +5 | Linear +1, +2, +3, +4, +5, +6 | 18 is wrong (should be 17) |
| 1, 8, 27, 64, 120, 216 | Cubes of 1, 2, 3, 4, 5, 6 | 120 | n³ (1³, 2³, 3³, 4³, 5³, 6³) | 120 is wrong (should be 125) |
| 4, 9, 19, 39, 79, 160 | +5, +10, +20, +40, +81 | +40 and +81 | × 2 + 1 (4, 9, 19, 39, 79, 159) | 160 is wrong (should be 159) |
Cadet Mnemonic • T-E-S-T Verification Check
T - Track the deltas, E - Expose the double fault, S - Substitute the real value, T - Total check confirms!
- 1. Track: Write out the full delta line.
- 2. Expose: The wrong number sits directly between the two corrupted deltas.
- 3. Substitute: Compute what the correct number must be.
- 4. Total check: Recalculate the next delta using your replacement to guarantee 100% certainty.
Exam Trick • Middle Term Rule for Wrong Numbers
If exactly three differences are normal at the start and two at the end, but the 4th and 5th differences are bizarre, the 5th number in the sequence is 100% the rogue term! Never spend more than 20 seconds guessing — just isolate the pivot point.
AISSEE Trap Alert • Don't Change the Rule to Fit the Wrong Number
A common mistake by students is creating an absurd, over-complicated mathematical equation just to justify a misprinted or rogue number. Always pick the simplest, most elegant rule that fits 80% of the terms, and flag the one exception as the wrong term!
Visual Concept Blueprint • Vector Architecture
Speed Shortcuts & Mental Calculation Strategies
Master these high-yield time-saving heuristics curated by top AISSEE scorers to eliminate calculation bottlenecks and answer questions in under 45 seconds.
Shortcut Technique 1: The First-Tier / Second-Tier Delta Protocol
Always calculate differences between consecutive terms in your exam margin. If Tier 1 differences don't show a clear rule, calculate Tier 2 differences immediately. Constant Tier 2 differences mean the series is quadratic (n²).
Shortcut Technique 2: The Split-Interleaved Scan
Whenever a sequence shows fluctuating values (e.g., up, down, up, down) or has more than 7 numbers, split it into two alternating sub-series (odd-positioned terms vs even-positioned terms) instantly.
Shortcut Technique 3: Continuous Letter Slot Factorization
For pattern filling (e.g., a_b_b_), count total letters and spaces first. If 12, divide by 3 or 4; if 15, divide by 3 or 5; if 16, divide by 4. Align chunks vertically to read identical columns.
Interactive 3D Revision Flashcards Deck
Click any card to flip and reveal the key exam rule or topper secret.
REVISION FLASHCARD
What does a constant second difference (Δ₂ = constant) indicate in a number series?
CADET MEMORY KEY
It indicates the sequence is a quadratic polynomial (related to n²). If Δ₂ = 2, the underlying series involves consecutive squares (n² ± k).
REVISION FLASHCARD
What are the first 7 terms of the classic n³ - n series?
CADET MEMORY KEY
0, 6, 24, 60, 120, 210, 336 (corresponding to 1³-1, 2³-2, 3³-3, 4³-4, 5³-5, 6³-6, 7³-7).
REVISION FLASHCARD
How do you solve an alternating interleaved series?
CADET MEMORY KEY
Separate the sequence into two independent sub-series: one with odd-positioned terms (1st, 3rd, 5th...) and one with even-positioned terms (2nd, 4th, 6th...).
REVISION FLASHCARD
What is the 'Rule of 27' in letter sequences?
CADET MEMORY KEY
The sum of a letter's forward rank (A=1) and its reverse rank from Z (Z=1) is always 27. Opposite pairs (A-Z, B-Y, C-X, M-N) always add up to 27.
REVISION FLASHCARD
How do you detect which number is wrong in a series?
CADET MEMORY KEY
Calculate the difference sequence. The single rogue number creates two adjacent abnormal difference values. The number lying between those two corrupted differences is the wrong term.
Common Traps & Examination Pitfalls
Avoid the Speed-Guess Trap: Under AISSEE pressure, candidates frequently misread units (e.g., mixing metres and centimetres, or per hour and per second) and confuse complementary ($90^\circ$) with supplementary ($180^\circ$) angles. Read every stem carefully and check units before selecting your OMR option.
Key Identities & Formulas
Linear Difference Rule
$$Tₙ₊₁ = Tₙ + (a + b·n)$$
Modified Cube Form
$$Tₙ = n³ - n = n(n - 1)(n + 1)$$
Rule of 27 for Reverse Letters
$$Forward Rank + Reverse Rank = 27$$
Step-by-Step Solved Examination Models
Solved Example 1
Model Problem
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Detailed Solution:
Step 1: Compute Tier-1 differences between consecutive terms:
• 11 - 4 = 7
• 25 - 11 = 14
• 46 - 25 = 21
• 74 - 46 = 28
Step 2: Observe the Tier-1 differences: 7, 14, 21, 28.
This is an arithmetic progression of multiples of 7 (+7 each time).
Step 3: The next Tier-1 difference must be 28 + 7 = 35.
Step 4: Add this difference to the last known term:
Next term = 74 + 35 = 109.
Answer: 109.
Solved Example 2
Model Problem
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Detailed Solution:
Step 1: Notice the numbers oscillate: 3 rises to 28, drops to 6, rises to 24, drops to 9. This indicates two interleaved series.
Step 2: Separate into odd-indexed and even-indexed positions:
• Series 1 (Positions 1, 3, 5, 7, 9): 3, 6, 9, 12, ?
• Series 2 (Positions 2, 4, 6, 8, 10): 28, 24, 20, 16, 12
Step 3: Analyze Series 1:
3 (+3) = 6 (+3) = 9 (+3) = 12 (+3) = 15.
Step 4: Check Series 2 for verification:
28 (-4) = 24 (-4) = 20 (-4) = 16 (-4) = 12 (verified).
Therefore, the missing term in position 9 is 15.
Answer: 15.
Solved Example 3
Model Problem
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Detailed Solution:
Step 1: Count total characters including blanks:
String: a [1] b a [2] b [3] b [4] a [5] b
Total characters = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12 characters.
Step 2: Factorize 12 into equal groups. Let's test groups of 3 and groups of 4:
Testing groups of 3: (a _ b) | (a _ b) | (_ b _) | (a _ b)
Notice the first group is 'a _ b', second is 'a _ b', fourth is 'a _ b'.
To make all groups identical, each group must be 'a b b'!
Step 3: Verify with 'a b b' for all 4 groups:
Group 1: a b b (blank 1 = b)
Group 2: a b b (blank 2 = b)
Group 3: a b b (blank 3 = a, blank 4 = b)
Group 4: a b b (blank 5 = b)
Step 4: Read off the inserted letters in sequential order:
Blank 1 = b, Blank 2 = b, Blank 3 = a, Blank 4 = b, Blank 5 = b.
Sequence = b, b, a, b, b.
Answer: b b a b b.
AISSEE High-Yield Practice Drills (10 Questions)
Simulated exam drill matching NTA question style, difficulty, and phrasing. Click an option for instant feedback and pedagogical explanation.
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Cadet Streak 🔥
Question 1 of 10
Exam Standard
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Correct Answer: Option (B)
Pattern: Each term is multiplied by 2 and then incremented by 1: 2 × 2 + 1 = 5; 5 × 2 + 1 = 11; 11 × 2 + 1 = 23; 23 × 2 + 1 = 47. Next term = 47 × 2 + 1 = 95.
Question 2 of 10
Exam Standard
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Correct Answer: Option (C)
Compute consecutive differences: 12 - 6 = 6; 21 - 12 = 9; 33 - 21 = 12; 48 - 33 = 15. The differences increase by +3 each step: 6, 9, 12, 15, 18. Next term = 48 + 18 = 66.
Question 3 of 10
Exam Standard
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Correct Answer: Option (A)
Pattern: n³ - 1. 1³ - 1 = 0; 2³ - 1 = 7; 3³ - 1 = 26; 4³ - 1 = 63; 5³ - 1 = 124; 6³ - 1 = 215. Next term = 7³ - 1 = 343 - 1 = 342.
Question 4 of 10
Exam Standard
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Correct Answer: Option (B)
Each term is the sum of the two preceding terms: 1 + 3 = 4; 3 + 4 = 7; 4 + 7 = 11; 7 + 11 = 18; 11 + 18 = 29. Next term = 18 + 29 = 47.
Question 5 of 10
Exam Standard
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Correct Answer: Option (B)
Convert letters to numeric ranks using EJOTY: B = 2, F = 6, J = 10, N = 14, R = 18. Each letter advances by +4. Next rank = 18 + 4 = 22 = V.
Question 6 of 10
Exam Standard
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Correct Answer: Option (A)
First letters: A(1) + 2 = C(3) + 2 = E(5) + 2 = G(7) + 2 = I(9). Second letters: Z(26) - 2 = X(24) - 2 = V(22) - 2 = T(20) - 2 = R(18). Notice each pair sums to 27 (reverse alphabet pairs). Target = IR.
Question 7 of 10
Exam Standard
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Correct Answer: Option (C)
Pattern: n² - 1. 2² - 1 = 3; 3² - 1 = 8; 4² - 1 = 15; 5² - 1 = 24; 6² - 1 = 35 (given as 34); 7² - 1 = 48; 8² - 1 = 63. The number 34 is incorrect; it should be 35.
Question 8 of 10
Exam Standard
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Correct Answer: Option (A)
First letter: A(1), C(3), E(5), G(7) → +2 step → I(9). Number: 2, 4, 8, 16 → ×2 step → 32. Second letter: B(2), D(4), F(6), H(8) → +2 step → J(10). Combining them yields I32J.
Question 9 of 10
Exam Standard
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Correct Answer: Option (B)
Total characters = 15. Divide into 5 groups of 3: (a b c) | (a c a is not uniform). Let's test 3 groups of 5 or cyclic pattern: (a b c c a) | (a b c c a) | (a b c c a) - exactly 15 characters! Filling blanks to make 'a b c c a': 1st blank = a, 2nd blank = b, 3rd blank = a, 4th blank = b, 5th blank = c. Sequence = a b a b c.
Question 10 of 10
Exam Standard
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Correct Answer: Option (B)
Method 1: Consecutive differences are 8, 16, 32, 64, 128. Missing term = 34 + 32 = 66. Verify next: 66 + 64 = 130 (correct). Method 2: Each term is × 2 - 2 (10×2 - 2 = 18; 18×2 - 2 = 34; 34×2 - 2 = 66). Both methods confirm 66.
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Frequently Asked Questions
How can I quickly identify whether a series is based on squares or cubes?
Look at the rate of growth. If the numbers grow moderately (e.g., reaching ~100 in 6 terms), suspect squares (n²). If the numbers explode rapidly (e.g., reaching 125, 216, 343 in just a few terms), test cubes (n³) immediately. Also check whether each term is 1 more or 1 less than a known perfect square or cube.
What should I do if a number series does not show any arithmetic or power pattern?
Check for: 1. Prime numbers (2, 3, 5, 7, 11, 13, 17); 2. Fibonacci-type addition (each term = sum of previous two terms); 3. Sum or product of the digits of each number; 4. Two interleaved alternating sequences running side-by-side.
In continuous letter series like a_b_b_, how do I know whether to group by 3 or 4?
Count total letters including blanks. If total is 12, try groups of 3 first, then 4. If total is 15, try groups of 3 or 5. If total is 16, it is almost invariably 4 groups of 4. Write the groups vertically one under another; matching columns will immediately reveal the repeating pattern.