Question 1

Number series (×n + n rule): compute the next term.  Sequence: 2, 3, 8, 27, 112, ?  At each step, multiply by the step index and add the same index. Choose the correct next value.

Accepted Answer

Rule ak+1 = ak·k + k (for k = 1, 2, 3, …) Verify 2 → 2·1 + 1 = 3 3 → 3·2 + 2 = 8 8 → 8·3 + 3 = 27 27 → 27·4 + 4 = 112 Next: 112 → 112·5 + 5 = 565

Question 2

Number series (increasing differences by 11): find the next term.  Sequence: 6, 17, 39, 72, ?  Compute the missing value using the difference pattern.

Accepted Answer

First differences 17 − 6 = 11 39 − 17 = 22 72 − 39 = 33 Next difference Add 11 each time ⇒ next = 33 + 11 = 44. Therefore next term = 72 + 44 = 116.

Question 3

Two interleaved sequences: fill the last two terms.  Series: 20, 20, 19, 16, 17, 13, 14, 11, ?, ?  Identify the odd/even position patterns and compute the missing pair.

Accepted Answer

Split into two subsequences Odd positions: 20, 19, 17, 14, ?, ? → differences: −1, −2, −3, −4, −5 ⇒ next terms: 14 − 4 = 10, then 10 − 5 = 5 Even positions: 20, 16, 13, 11, ?, ? → differences: −4, −3, −2, −1, 0 ⇒ next terms: 11 − 1 = 10, then 10 − 0 = 10 Assemble the sequence … 14, 11, 10, 10 Note The question asks for the last two terms (positions 9 and 10), which are 10 and 10.

Question 4

Product of three consecutive integers: find the next term.  Sequence: 24, 60, 120, 210, ?  Each term equals n·(n+1)·(n+2) for increasing n. Choose the next value.

Accepted Answer

Identify terms 24 = 2·3·4 60 = 3·4·5 120 = 4·5·6 210 = 5·6·7 Next term n = 6 ⇒ 6·7·8 = 336

Question 5

Powers of 5 interleaved: determine the missing term.  Sequence: 625, 5, 125, 25, 25, ?, 5  Recognize the pattern via exponents of 5 and fill in the blank.

Accepted Answer

Rewrite in powers of 5 625 = 5⁴, 5 = 5¹, 125 = 5³, 25 = 5², 25 = 5², ? = 5³, 5 = 5¹. Pattern Exponents follow 4, 1, 3, 2, 2, 3, 1 (a mirrored/paired arrangement around 2). Missing term Therefore ? = 5³ = 125.

Question 6

Increasing increments by 10: find the next term.  Sequence: 10, 100, 200, 310, ?  Differences grow by 10 each step. Choose the correct next value.

Accepted Answer

First differences 100 − 10 = 90 200 − 100 = 100 310 − 200 = 110 Next difference Add 10 again ⇒ 120; 310 + 120 = 430.

Question 7

Number series (pattern with binary-like digit toggling): Find the missing term that preserves the 1–0 structure.  Given sequence: 11, 10, ?, 100, 1001, 1000, 10001 Observation: terms alternately change the last digit to 0, then append a 1. Choose th…

Accepted Answer

Given data 11, 10, ?, 100, 1001, 1000, 10001 Concept/Approach The sequence is built by two alternating operations on the digit string: (i) change the last digit to 0, then (ii) append a trailing 1. This keeps a binary-like pattern of 1s and 0s. Step-by-step Start: 11Operation (i): 11 → 10 (last digit set to 0)Operation (ii): 10 → 101 (append 1) ← missing termOperation (i): 101 → 100Operation (ii): 100 → 1001Operation (i): 1001 → 1000Operation (ii): 1000 → 10001 Final Answer 101

Question 8

Number series (next term by repeated ×4 − 1 rule): Determine the next value.  Given sequence: 2, 7, 27, 107, 427, ? Pattern hint: each term equals (previous term × 4) − 1. Choose the correct next number.

Accepted Answer

Given data 2, 7, 27, 107, 427, ? Concept/Approach Test a simple linear recurrence of the form an+1 = 4an − 1. Step-by-step 2 × 4 − 1 = 77 × 4 − 1 = 2727 × 4 − 1 = 107107 × 4 − 1 = 427Next: 427 × 4 − 1 = 1708 − 1 = 1707 Verification The rule holds for every transition; applying once more yields 1707.

Question 9

Find the missing term in the factorial pattern: 1, 1, 2, 6, 24, ?, 720

Accepted Answer

Introduction / Context: This is a sequence recognition question. The numbers resemble factorials, which are products of all positive integers up to a given n. Recognizing the pattern lets us supply the missing term. Given Data / Assumptions: Sequence: 1, 1, 2, 6, 24, ?, 720. Consecutive terms increase rapidly, suggesting factorial growth. Concept / Approach: Recall factorial definition: n! = 1 * 2 * 3 * ... * n. Note small factorials: 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720. Map these to the given sequence to identify the missing value. Step-by-Step Solution: Identify terms: 1 (0!), 1 (1!), 2 (2!), 6 (3!), 24 (4!), ? (5!), 720 (6!).Thus the missing term is 5! = 120. Verification / Alternative check: Compute 6! = 720 matches the last term, confirming factorial interpretation and validating 5! = 120 as the missing entry. Why Other Options Are Wrong: 100, 104, 108, 144: None are equal to 5! and do not fit the factorial pattern. Common Pitfalls: Forgetting that both 0! and 1! equal 1, which explains the first two terms. Final Answer: 120

Question 10

Number series — find the next two terms. Sequence: 2, 15, 4, 12, 6, 7, ?, ?

Accepted Answer

Introduction / Context: This is a number-series question that tests pattern recognition with interleaved (alternating) subsequences. Many competitive exams hide two simpler progressions inside a single list. Spotting and separating those strands is the key skill being assessed. Given Data / Assumptions: Given sequence: 2, 15, 4, 12, 6, 7, ?, ? We assume a deterministic numeric pattern without external data. We consider the possibility of two alternating subsequences (odd/even positions). Concept / Approach: Split the sequence into terms at odd and even positions to see if each forms a simpler rule. Odd positions: 1st, 3rd, 5th, 7th. Even positions: 2nd, 4th, 6th, 8th. Look for simple arithmetic changes such as constant addition/subtraction steps or small linear rules. Step-by-Step Solution: Odd-position terms: 2 (1st), 4 (3rd), 6 (5th), ? (7th). Pattern is +2 each step, so the 7th term = 6 + 2 = 8. Even-position terms: 15 (2nd), 12 (4th), 7 (6th), ? (8th). Differences are −3 then −5; a common progression here is subtracting consecutive odd numbers: −3, −5, next −7. Compute 8th term: 7 − 7 = 0. Verification / Alternative check: Rebuild the full sequence with the derived terms: 2, 15, 4, 12, 6, 7, 8, 0. Each subsequence consistently follows its rule (+2 for odds, −3/−5/−7 for evens). Why Other Options Are Wrong: 8, 8: Correct 7th term but ignores the even-position decreasing pattern. 3, 8: Breaks the steady +2 rule in the odd positions. None of these: Not applicable since 8, 0 fits perfectly. Common Pitfalls: Mixing positions or trying to force a single-step rule across all terms rather than splitting into alternating strands. Final Answer: 8, 0

Question 11

Number series — complete the sequence. Sequence: 4832, 5840, 6848, ?

Accepted Answer

Introduction / Context: This problem focuses on recognizing a constant difference across terms (an arithmetic progression in large steps). Identifying the increment and applying it forward yields the missing number efficiently. Given Data / Assumptions: Known terms: 4832, 5840, 6848. We test for constant addition between consecutive terms. No digit tricks are necessary if a clean common difference appears. Concept / Approach: Compute pairwise differences. If the differences are equal, the sequence is arithmetic with that common step. Then add the same step to the last given term to obtain the next value. Step-by-Step Solution: Difference 1: 5840 − 4832 = 1008. Difference 2: 6848 − 5840 = 1008. Common difference confirmed: 1008. Next term = 6848 + 1008 = 7856. Verification / Alternative check: Re-run subtraction to confirm: 7856 − 6848 = 1008, preserving the arithmetic pattern. No anomalies in carry or borrow operations occur. Why Other Options Are Wrong: 7815/7846/7887: None equal 6848 + 1008; thus they break the constant step of 1008. Common Pitfalls: Overcomplicating with digit manipulations (reversals, inter-digit sums) when a simple constant difference fits perfectly. Final Answer: 7856

Question 12

Number series — find the missing middle term. Sequence: 5824, 5242, ?, 4247, 3823

Accepted Answer

Introduction / Context: Some four-digit series are built by treating the first two digits and the last two digits as separate subseries evolving in parallel. The challenge is to decode each pair’s rule and then merge them to reconstruct the missing term. Given Data / Assumptions: Sequence: 5824, 5242, ?, 4247, 3823. Observation: The first two digits (left pair) and last two digits (right pair) appear to follow independent patterns. We assume consistent pairwise evolution across the list. Concept / Approach: Split each term into LeftPair|RightPair. Track left pairs: 58, 52, __, 42, 38. Track right pairs: 24, 42, __, 47, 23. Identify simple arithmetic changes for each side (e.g., alternating decrements). Step-by-Step Solution: Left pairs: 58 → 52 (−6), 52 → 48 (−4), 48 → 42 (−6), 42 → 38 (−4). Pattern alternates −6, −4, −6, −4. Therefore, the missing left pair is 48. Right pairs given: 24 → 42 (+18), __ → 47, 47 → 23 (−24). The only option whose right pair fits a reasonable stepping from 42 and allows continuation to 47 is 56 (i.e., +14 from 42, then −9 to 47), which appears in 4856. Thus the missing term is 4856. Verification / Alternative check: Assemble the sequence with 4856: 5824, 5242, 4856, 4247, 3823. The left side maintains its alternating −6/−4 rhythm; the right side shows plausible step downs to reach 47 and then 23. Why Other Options Are Wrong: 4467/4718/5164: Their left pairs break the −6/−4 alternation (should be 48), so they cannot fit. Common Pitfalls: Focusing only on whole-number differences and missing the left/right pair decomposition that actually drives the pattern. Final Answer: 4856

Question 13

Number series — determine the next term. Sequence: 2, 8, 16, 128, ?

Accepted Answer

Introduction / Context: This item examines recognition of multiplicative jumps driven by powers of 2. Many exam series interleave different multipliers; spotting the power pattern quickly leads to the correct continuation. Given Data / Assumptions: Terms: 2, 8, 16, 128, ? All given terms are powers of 2 or products that can be expressed with powers of 2. We look for a multiplier pattern consistent with powers of 2. Concept / Approach: Inspect transitions: 2 → 8 (×4), 8 → 16 (×2), 16 → 128 (×8). The multipliers themselves are 4, 2, 8 which are 2^2, 2^1, 2^3. A natural continuation is to apply the next increasing power 2^4 = 16 to 128. Step-by-Step Solution: Identify multiplier sequence as powers of 2: 2^2, 2^1, 2^3, 2^4 ... Compute next term: 128 × 16 = 2048. Check internal consistency: each jump uses a power of 2; the exponents visited (2,1,3,4) include a plausible step-up to 4 next. Verification / Alternative check: 2048 is itself 2^11; the rapid growth matches the observed leap from 16 to 128 (×8). Why Other Options Are Wrong: 2042/2046/2056: Not powers of 2 and not equal to 128 × 2^k for integer k; they break the power-of-two multiplier theme. Common Pitfalls: Expecting constant multipliers or trying to add instead of multiply, which cannot produce 128 from 16 without a large inconsistent jump. Final Answer: 2048

Question 14

Number series — continue the pattern. Sequence: 1, 2, 6, 7, 21, 22, 66, 67, ?

Accepted Answer

Introduction / Context: This sequence alternates between multiplying by 3 and then adding 1. Such two-step cycles are common in reasoning tests. Recognizing the cycle allows you to project the next value confidently. Given Data / Assumptions: Sequence chunks appear as pairs: (1, 2), (6, 7), (21, 22), (66, 67)... Within each pair, the first number seems to be tripled from a previous term, and the second number is that result plus 1. We extend the same two-step rule forward. Concept / Approach: Identify the repeating cycle: ×3, then +1. Apply it from the last two numbers to determine the next. Step-by-Step Solution: From 66 to 67 is +1, completing a pair. The next step starts a new pair by applying ×3 to 67: 67 × 3 = 201. Thus the next term (the first of the new pair) is 201. Verification / Alternative check: Check earlier transitions: 2 → 6 (×3), 6 → 7 (+1); 7 → 21 (×3), 21 → 22 (+1); 22 → 66 (×3), 66 → 67 (+1). Pattern is consistent. Why Other Options Are Wrong: 70/134/301: Do not equal 67 × 3. They would break the ×3, +1 alternation that fits every prior pair. Common Pitfalls: Applying +1 again after 67, forgetting the cycle restarts with ×3. Final Answer: 201

Question 15

Number series — determine the next value. Sequence: 0.5, 0.55, 0.65, 0.8, ?

Accepted Answer

Introduction / Context: Decimal series frequently use steadily increasing increments. Here, the step sizes themselves grow in a simple arithmetic fashion. Recognizing the step pattern yields the next term quickly and accurately. Given Data / Assumptions: Sequence: 0.5, 0.55, 0.65, 0.8, ? We check consecutive differences. Assume a simple incremental pattern across steps. Concept / Approach: Compute differences: 0.55 − 0.5 = 0.05; 0.65 − 0.55 = 0.10; 0.8 − 0.65 = 0.15. The increases are 0.05, 0.10, 0.15 — a clear arithmetic sequence with common difference 0.05. The next increase should be 0.20. Step-by-Step Solution: Identify step sizes: +0.05, +0.10, +0.15. Next step = previous step + 0.05 = 0.20. Next term = 0.8 + 0.20 = 1.0. Verification / Alternative check: Extending the differences gives 0.05, 0.10, 0.15, 0.20 — consistent linear growth of step size by 0.05. Why Other Options Are Wrong: 0.9/0.95/0.82: Do not reflect a +0.20 jump from 0.8; they would imply inconsistent step sizes. Common Pitfalls: Averaging terms or assuming constant difference, missing the steadily increasing increments (0.05 added each time to the step). Final Answer: 1

Question 16

Number series — fill in the next term. Sequence: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?

Accepted Answer

Introduction / Context: This sequence mixes two alternating increment patterns: a constant small jump and a steadily increasing odd-number jump. Detecting the alternation allows you to continue the series with confidence. Given Data / Assumptions: Sequence: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ? We analyze consecutive differences. We expect an alternating motif. Concept / Approach: Compute term-to-term differences: +2, +1, +2, +3, +2, +5, +2, +7, +2, ?. The pattern alternates +2 with ascending odd numbers: +1, +3, +5, +7, +9, ... Therefore, after the last +2, the next jump should be +9. Step-by-Step Solution: List differences: 0→2 (+2), 2→3 (+1), 3→5 (+2), 5→8 (+3), 8→10 (+2), 10→15 (+5), 15→17 (+2), 17→24 (+7), 24→26 (+2). Following the rule, next increase = +9. Compute next term: 26 + 9 = 35. Verification / Alternative check: The odd increments form a clear sequence 1, 3, 5, 7, 9. Interleaving with +2 confirms the structure holds throughout. Why Other Options Are Wrong: 28/30/32: Correspond to +2, +4, +6 changes, which would break the established alternating +2, +(odd growing) scheme. Common Pitfalls: Assuming a single constant difference or missing the interleaving of two separate incremental rules. Final Answer: 35

Question 17

Number series — choose the next term. Sequence: 11, 13, 17, 19, 23, 25, ?

Accepted Answer

Introduction / Context: The sequence alternates between adding 2 and adding 4, a common construction that mostly tracks prime-like steps but includes a non-prime deliberately to cue attention to the step sizes rather than primality. Given Data / Assumptions: Terms: 11, 13, 17, 19, 23, 25, ? We focus on differences, not on primality alone (since 25 is not prime). Concept / Approach: Compute successive differences: 13 − 11 = 2; 17 − 13 = 4; 19 − 17 = 2; 23 − 19 = 4; 25 − 23 = 2. The pattern clearly alternates +2, +4, +2, +4, +2, so the next difference should be +4. Step-by-Step Solution: Apply the alternating increment: after +2 to reach 25, next add +4. Next term = 25 + 4 = 29. Check continuity across all terms to ensure the alternation is unbroken. Verification / Alternative check: Reconstructing: 11 (+2) 13 (+4) 17 (+2) 19 (+4) 23 (+2) 25 (+4) 29 confirms the pattern. Why Other Options Are Wrong: 26/27/37: Do not equal 25 + 4; they would violate the +2/+4 alternation. Common Pitfalls: Assuming “next prime” after 23 and being confused by 25; the rule is increments, not primality. Final Answer: 29

Question 18

Number series — continue the Fibonacci-like pattern. Sequence: 5, 2, 7, 9, 16, 25, ?

Accepted Answer

Introduction / Context: This is a sum-of-previous-two sequence (a Fibonacci-style recurrence) but started with custom seed values. Many exam sets include such recurrences where each term equals the sum of the two immediately preceding terms. Given Data / Assumptions: Sequence given: 5, 2, 7, 9, 16, 25, ? We test the recurrence a(n) = a(n−1) + a(n−2). Concept / Approach: Verify the rule across each step: 5 + 2 = 7, 2 + 7 = 9, 7 + 9 = 16, 9 + 16 = 25. If consistent, compute the next as 16 + 25. Step-by-Step Solution: Check term 3: 5 + 2 = 7 (fits). Term 4: 2 + 7 = 9 (fits). Term 5: 7 + 9 = 16 (fits). Term 6: 9 + 16 = 25 (fits). Next term: 16 + 25 = 41. Verification / Alternative check: Continue one more step mentally: after 41, the next would be 25 + 41 = 66, reinforcing that the rule holds. Why Other Options Are Wrong: 45/48/52: None equals 16 + 25; they violate the “sum of last two” rule. Common Pitfalls: Looking for multiplicative patterns or alternating sequences, when a simple two-term sum explains all transitions. Final Answer: 41

Question 19

Number series — find the next term using second-difference logic. Sequence: 7, 26, 63, 124, 215, 342, ?

Accepted Answer

Introduction / Context: Many non-linear sequences grow via increasing differences; the differences themselves follow a clear pattern. Detecting that the second differences are in arithmetic progression allows you to project the next first difference and hence the next term. Given Data / Assumptions: Sequence: 7, 26, 63, 124, 215, 342, ? We examine first differences and then second differences. Concept / Approach: Compute first differences: 26−7=19, 63−26=37, 124−63=61, 215−124=91, 342−215=127. Now compute second differences between these: 37−19=18, 61−37=24, 91−61=30, 127−91=36. These second differences increase by +6 each time (18, 24, 30, 36, next 42). Step-by-Step Solution: First differences so far: 19, 37, 61, 91, 127. Second differences: +18, +24, +30, +36 (step +6). Next second difference = 36 + 6 = 42. Next first difference = last first difference + next second difference = 127 + 42 = 169. Next term = last term + next first difference = 342 + 169 = 511. Verification / Alternative check: 169 is 13^2, which often appears in such crafted puzzles; adding it to 342 produces 511, a value consistent with the accelerating growth observed. Why Other Options Are Wrong: 391/421/481: These would imply different first differences that break the +6 pattern in second differences. Common Pitfalls: Trying to match powers or products directly without checking the structured growth of differences. Final Answer: 511

Question 20

Number Series — Find the Next Term Identify the next number in the sequence: 3, 12, 27, 48, 75, 108, ?

Accepted Answer

Introduction / Context: This is a classic number series question where the pattern is based on successive differences. Recognizing difference patterns is a fundamental technique in quantitative aptitude and competitive exams. Given Data / Assumptions: Series terms: 3, 12, 27, 48, 75, 108, ? We assume a deterministic arithmetic pattern in first or higher-order differences. Concept / Approach: Check consecutive differences. If differences themselves follow a clear progression (such as an arithmetic sequence), extend that progression to get the next difference, then add it to the last known term to obtain the answer. Step-by-Step Solution: Compute differences: 12 − 3 = 927 − 12 = 1548 − 27 = 2175 − 48 = 27108 − 75 = 33The difference sequence is: 9, 15, 21, 27, 33These increase by 6 each time: 9 + 6 = 15, 15 + 6 = 21, ... , 27 + 6 = 33Next difference = 33 + 6 = 39Next term = last term + next difference = 108 + 39 = 147 Verification / Alternative check: Observe that differences form an arithmetic progression with common difference 6. Extending once yields 39, confirming 147 as consistent with the pattern. Why Other Options Are Wrong: 162, 183, 192: None are equal to 108 + 39; they violate the established difference pattern. Common Pitfalls: Jumping to a multiplicative pattern or skipping the check on differences. Always test first differences (and, if needed, second differences) before trying more complex patterns. Final Answer: 147

Series Completion Questions