Question 1

Number set — pick the odd number out (all others are composite): 4, 6, 8, 9, 10, 11, 12

Accepted Answer

Introduction / Context:This is a property-based odd-one-out question. The simplest distinguishing feature among the listed integers is “prime vs. composite.” Identify the only prime to find the outlier. Given Data / Assumptions: Numbers: 4, 6, 8, 9, 10, 11, 12 Exactly one should be different by a basic number-theory property. Concept / Approach:Check primality. A prime has exactly two positive divisors (1 and itself). Composite numbers have more than two factors. Quickly factor each number to classify it. Step-by-Step Solution: 4 = 22 → composite6 = 23 → composite8 = 222 → composite9 = 33 → composite10 = 25 → composite11 → prime (only 1 and 11 divide 11)12 = 223 → compositeThus 11 is the only prime; all others are composite. Verification / Alternative check: Try any divisibility tests: 11 is not divisible by 2, 3, 5; hence prime in this range. Why Other Options Are Wrong: 4, 6, 8, 9, 10, 12 each has nontrivial factors; none is prime. Common Pitfalls: Mistaking 9 (a perfect square) for prime — it is composite (3*3). Final Answer:11

Question 2

Number series — find the odd term (decrements should reduce by +5 each step): 105, 85, 60, 30, 0, -45, -90

Accepted Answer

Introduction / Context:Here we have a decreasing series. Many such sequences reduce by amounts that grow steadily (e.g., −20, −25, −30, −35…). If one reduction breaks the step-size pattern, the corresponding term is the odd one out. Given Data / Assumptions: Series: 105, 85, 60, 30, 0, −45, −90 One term does not fit the intended decrement pattern. Concept / Approach:Compute consecutive differences and verify whether the decrements increase by 5 each time (a common construction). Identify any mismatch. Step-by-Step Solution: 85 − 105 = −2060 − 85 = −2530 − 60 = −300 − 30 = −30 (should be −35 here)−45 − 0 = −45 (this would match the next step if previous were correct)−90 − (−45) = −45 (should then be −50 if strictly continuing)The fourth step should be −35, making 30 − 35 = −5, not 0. Thus 0 is the inconsistent term. Verification / Alternative check: Corrected sequence with −20, −25, −30, −35, −40, −45 steps: 105, 85, 60, 30, −5, −45, −90. Why Other Options Are Wrong: 85, 60 align with −20 and −25; −45 and −90 can align with larger negative steps; they are plausible under the corrected pattern. Common Pitfalls: Accepting repeated −30 steps without checking the expected growth in decrement size. Final Answer:0

Question 3

Number pattern — identify the odd term in the alternating pattern: 5, 16, 6, 16, 7, 16, 9

Accepted Answer

Introduction / Context:This sequence alternates between a changing number and a fixed number. Detecting the alternating positions (odd/even indices) quickly reveals which entry is inconsistent. Given Data / Assumptions: Sequence: 5, 16, 6, 16, 7, 16, 9 Positions: 1st, 3rd, 5th, 7th terms are the varying stream; 2nd, 4th, 6th terms are constant. Concept / Approach:Read terms in two interleaved subsequences: one fixed at 16, the other apparently increasing by 1 each occurrence. Any break in either subsequence marks the odd term. Step-by-Step Solution: Fixed subsequence (even positions): 16, 16, 16 — consistent.Varying subsequence (odd positions): 5 → 6 → 7 → expected 8.But the last odd-position term is 9, which skips 8.Therefore, 9 is the odd term. Verification / Alternative check: Corrected sequence would be 5, 16, 6, 16, 7, 16, 8. Why Other Options Are Wrong: 7 and 6 fit the +1 progression; “None of these” is incorrect because a clear outlier (9) exists. Common Pitfalls: Treating the series as a single arithmetic progression rather than two interwoven sub-series. Final Answer:9

Question 4

Number series — pick the odd term (increments should be successive primes): 125, 127, 130, 135, 142, 153, 165

Accepted Answer

Introduction / Context:Another common construction uses increments equal to consecutive prime numbers. If a final step uses the wrong increment, that last term becomes the odd one out. Given Data / Assumptions: Series: 125, 127, 130, 135, 142, 153, 165 Increments suspected: +2, +3, +5, +7, +11, +13… Concept / Approach:Compute consecutive differences and map them to the prime list. Any mismatch will surface immediately. Step-by-Step Solution: 127 − 125 = +2 (prime)130 − 127 = +3 (prime)135 − 130 = +5 (prime)142 − 135 = +7 (prime)153 − 142 = +11 (prime)165 − 153 = +12 (should be +13 next)Therefore, the correct last term should be 153 + 13 = 166. The given 165 is off by −1 and is the outlier. Verification / Alternative check: Replacing 165 with 166 yields perfect prime increments: +2, +3, +5, +7, +11, +13. Why Other Options Are Wrong: 130, 142, 153 all fit prime-step increments; they are consistent with the intended rule. Common Pitfalls: Confusing near-prime increments (like +12) with the actual next prime +13. Final Answer:165

Question 5

Number series – find the wrong term (identify the outlier). Sequence: 46080, 3840, 384, 48, 24, 2, 1

Accepted Answer

Introduction / Context:Many competitive exams include number series questions where one term does not follow the rule that generates the rest. The task is to detect the underlying operation pattern and identify the incorrect term that breaks it. Given Data / Assumptions: Series provided: 46080, 3840, 384, 48, 24, 2, 1 Exactly one term is wrong. Operations are typically clean integer operations such as multiplication or division by a steadily changing factor. Concept / Approach:Look at consecutive ratios or divisors. In many decreasing sequences, each term is derived by dividing the previous term by a changing even number or by a consistent pattern such as dividing by descending even integers. Step-by-Step Solution: Compute ratios: 46080/3840 = 12.3840/384 = 10.384/48 = 8.Expected next divisor if pattern is descending even numbers is 6, so 48/6 = 8 is expected.But given term is 24, which corresponds to dividing by 2, breaking the pattern.Continuing the intended pattern: after divide by 6 should come divide by 4 then divide by 2, ending at 2 then 1. Verification / Alternative check:If we replace 24 with 8, the sequence of divisors becomes 12, 10, 8, 6, 4, 2 which is perfectly regular. This confirms 24 is the anomaly. Why Other Options Are Wrong: 1 and 2: They fit the final steps of dividing by 2 repeatedly at the end of the descending pattern. 384: Matches division by 10 from 3840 correctly. Common Pitfalls:Focusing only on differences rather than ratios can hide a clean divisor pattern. Always check both differences and ratios. Final Answer:24

Question 6

Number series – find the wrong term (identify the outlier). Sequence: 6, 13, 18, 25, 30, 37, 40

Accepted Answer

Introduction / Context:The goal is to detect the underlying rule that generates the series. Typically, simple addition with alternating steps is used in such problems, and one term may be deliberately incorrect. Given Data / Assumptions: Series: 6, 13, 18, 25, 30, 37, 40 Exactly one term is wrong. Concept / Approach:Check for a repeating increment pattern. Alternating additions such as +7, +5 are very common. Confirm whether each step aligns with that pattern. Step-by-Step Solution: 6 + 7 = 13 (fits +7)13 + 5 = 18 (fits +5)18 + 7 = 25 (fits +7)25 + 5 = 30 (fits +5)30 + 7 = 37 (fits +7)Expected next step is +5, so 37 + 5 = 42.Given term is 40, which breaks the +7, +5 alternating pattern. Verification / Alternative check:Reconstruct the intended series: 6, 13, 18, 25, 30, 37, 42. This confirms 40 is the only inconsistent term. Why Other Options Are Wrong: 25 and 30: Precisely match the alternating +7, +5 increments. 37: Also correct as the +7 step after 30. Common Pitfalls:Computing differences inconsistently or skipping a step in the pattern. Always confirm the alternating cycle across multiple transitions. Final Answer:40

Question 7

Number series – find the wrong term (identify the outlier). Sequence: 36, 54, 18, 27, 9, 18.5, 4.5

Accepted Answer

Introduction / Context:Series may alternate two different operations. Here the task is to detect the alternating rule and find which term violates it. Given Data / Assumptions: Series: 36, 54, 18, 27, 9, 18.5, 4.5 Exactly one term is wrong. Concept / Approach:Check whether the sequence alternates between multiplying and dividing by a constant factor. Multiplying by 1.5 and then dividing by 3 is a common alternating pair because 1.5 and 1/3 are inverses over two steps in a ratio sense. Step-by-Step Solution: 36 * 1.5 = 54 (correct)54 / 3 = 18 (correct)18 * 1.5 = 27 (correct)27 / 3 = 9 (correct)Next by rule: 9 * 1.5 = 13.5 (expected)But given term is 18.5, which does not match the rule.Continuing the intended pattern: after 13.5, dividing by 3 gives 4.5, which matches the final term. Verification / Alternative check:Replace 18.5 with 13.5 and verify the full alternating pattern holds end to end. It does, confirming 18.5 is the outlier. Why Other Options Are Wrong: 54, 18, 4.5: Each aligns with the alternating multiply by 1.5 and divide by 3 rule. Common Pitfalls:Comparing only differences instead of ratios can hide multiplicative patterns. Always test ratio-based operations in geometric series. Final Answer:18.5

Question 8

Number series – find the wrong term (identify the outlier). Sequence: 56, 72, 90, 110, 132, 150

Accepted Answer

Introduction / Context:This is a difference-pattern series where each step increases by a steadily growing even number. One term breaks the pattern and must be identified. Given Data / Assumptions: Series: 56, 72, 90, 110, 132, 150 One term is incorrect. Concept / Approach:Compute successive differences and check whether they follow a simple progression, such as adding even numbers that increase by 2 each time. Step-by-Step Solution: 72 − 56 = 1690 − 72 = 18110 − 90 = 20132 − 110 = 22Expected next difference is 24, so expected next term = 132 + 24 = 156.Given final term is 150, which is short by 6 and breaks the +2-increment pattern of the differences. Verification / Alternative check:Replace 150 with 156 to obtain differences 16, 18, 20, 22, 24, a consistent arithmetic progression of even numbers. Why Other Options Are Wrong: 72, 110, 132: Each fits perfectly into the growing-difference pattern. Common Pitfalls:Looking at ratios when the structure is additive. Always test both methods, but here differences immediately reveal the rule. Final Answer:150

Question 9

Number series – find the wrong term (identify the outlier). Sequence: 25, 36, 49, 81, 121, 169, 225

Accepted Answer

Introduction / Context:This series contains perfect squares. The task is to identify which square does not belong to the intended pattern once the underlying rule is recognized. Given Data / Assumptions: Squares listed: 25, 36, 49, 81, 121, 169, 225 Only one term is wrong with respect to the intended sequence logic. Concept / Approach:Note that 25 = 5^2, 49 = 7^2, 81 = 9^2, 121 = 11^2, 169 = 13^2, 225 = 15^2. These are consecutive odd squares starting at 5^2, except one even square appears in the list. Step-by-Step Solution: Identify the intended pattern: squares of odd integers from 5 upward.List intended terms: 5^2 = 25, 7^2 = 49, 9^2 = 81, 11^2 = 121, 13^2 = 169, 15^2 = 225.Compare with the given sequence and spot 36 = 6^2, which is an even square breaking the odd-only pattern. Verification / Alternative check:Remove 36 and the remaining sequence consists entirely of odd squares in ascending order. No other term violates that rule. Why Other Options Are Wrong: 49, 121, 169: Each is a square of an odd integer and thus fits the intended pattern. Common Pitfalls:Assuming the series is simply all consecutive squares. The presence of 36 can mislead; look for a deeper consistency such as only odd squares. Final Answer:36

Question 10

Number series – find the next term. Sequence: 16, 33, 65, 131, 261, ( ? )

Accepted Answer

Introduction / Context:Next-term series often alternate between two closely related operations. Recognizing the alternation is key to predicting the following number with confidence. Given Data / Assumptions: Sequence terms: 16, 33, 65, 131, 261 We need the next term. Concept / Approach:Test a pattern of doubling with small adjustments. A classic alternation is multiply by 2 then add 1, followed by multiply by 2 then subtract 1, repeating. Step-by-Step Solution: 16 * 2 + 1 = 3333 * 2 − 1 = 6565 * 2 + 1 = 131131 * 2 − 1 = 261Next continues the alternation: 261 * 2 + 1 = 523 Verification / Alternative check:Check parity: the +1 steps produce odd numbers, and the −1 steps also produce odd numbers, consistent with all terms being odd except the first. The alternating adjustments confirm the rule. Why Other Options Are Wrong: 521, 613, 721: These do not follow the multiply by 2 with alternating ±1 rule from the previous term 261. Common Pitfalls:Trying constant differences or ratios. The near doubling suggests testing a slight alternating offset from exact 2x. Final Answer:523

Question 11

Number series – find the next term. Sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )

Accepted Answer

Introduction / Context:Many number series interleave two independent subsequences at odd and even positions. Isolating each subsequence often reveals simple patterns that make the next term obvious. Given Data / Assumptions: Overall sequence: 10, 5, 13, 10, 16, 20, 19, ( ? ) We expect two interleaved patterns: one for odd positions, one for even positions. Concept / Approach:Separate odd-indexed terms and even-indexed terms and analyze each independently. Common rules include constant increments for one and doubling or halving for the other. Step-by-Step Solution: Odd positions (1st, 3rd, 5th, 7th): 10, 13, 16, 19 – this is +3 each time.Even positions (2nd, 4th, 6th): 5, 10, 20 – this is times 2 each step.The next term is the 8th term (even position), so apply the even-position rule: 20 * 2 = 40. Verification / Alternative check:Project forward: if a 9th term were needed (odd position), it would be 19 + 3 = 22, which is consistent, reinforcing the correctness of the extracted rules. Why Other Options Are Wrong: 22: That would be correct for the next odd position, not the 8th term. 38 and 23: Do not follow either identified rule from the immediately prior relevant subsequence term. Common Pitfalls:Trying to force a single-step rule on the entire sequence rather than splitting into interleaved streams. Final Answer:40

Question 12

Number series – find the next term. Sequence: 1, 4, 9, 16, 25, 36, 49, ( ? )

Accepted Answer

Introduction / Context:This sequence is the classic list of perfect squares in ascending order. Recognizing square numbers is a foundational skill in quantitative reasoning questions. Given Data / Assumptions: Given terms: 1, 4, 9, 16, 25, 36, 49 These are 1^2 through 7^2. Concept / Approach:Perfect squares follow n^2 for integer n. The next integer after 7 is 8, therefore the next square is 8^2. Step-by-Step Solution: Identify n values: 1, 2, 3, 4, 5, 6, 7.Compute next: 8^2 = 64. Verification / Alternative check:Confirm earlier values: 6^2 = 36 and 7^2 = 49. The progression is consistent, so 8^2 is the next logical term. Why Other Options Are Wrong: 54 and 56: Not perfect squares. 81: That is 9^2, which would be the term after 64, not immediately next to 49 if stepping by single integers. Common Pitfalls:Confusing square numbers with triangular or other figurate numbers. Always check n^2 explicitly. Final Answer:64

Question 13

Number series – find the next term. Sequence: 2, 4, 12, 48, 240, ( ? )

Accepted Answer

Introduction / Context:Product series frequently multiply by increasing integers. Detecting the multiplying factors allows quick prediction of the next term. Given Data / Assumptions: Sequence: 2, 4, 12, 48, 240 We need the sixth term. Concept / Approach:Check ratios between successive terms: they may be 2, 3, 4, 5, suggesting the next ratio is 6. Such factorial-like growth is common in exam problems. Step-by-Step Solution: 2 * 2 = 44 * 3 = 1212 * 4 = 4848 * 5 = 240Next factor is 6: 240 * 6 = 1440 Verification / Alternative check:List multipliers: 2, 3, 4, 5, 6. They form a simple ascending integer sequence, confirming the logic. Why Other Options Are Wrong: 960: Would imply multiplying by 4 again, breaking the increasing-factor pattern. 1080: Would correspond to multiplying by 4.5, not an integer step. 1920: Would be 240 * 8, skipping the expected factor 6. Common Pitfalls:Assuming constant ratio. Here the ratio itself increases by 1 each step. Final Answer:1440

Question 14

Number series – find the next term. Sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? )

Accepted Answer

Introduction / Context:This sequence is formed by interleaving two simpler subsequences. Identifying and separating them is the key step to determining the next number. Given Data / Assumptions: Main sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? ) Terms at odd positions and even positions likely follow different rules. Concept / Approach:Extract the odd-position subsequence and the even-position subsequence. Analyze each for a consistent add pattern. Step-by-Step Solution: Odd positions (1,3,5,7): 8, 11, 14, 17 – this increases by +3 each time.Even positions (2,4,6,8): 7, 12, 17, 22 – this increases by +5 each time.The next term is the 9th (odd position), so apply the odd-position rule: 17 + 3 = 20. Verification / Alternative check:Project the even sequence further: after 22 would come 27, which matches option 27 but would be the 10th term, not the 9th. This cross-check supports 20 as the correct immediate next value. Why Other Options Are Wrong: 27: Correct for the 10th term (even position), not for the 9th. 22 and 24: Do not match the +3 increment needed at odd positions after 17. Common Pitfalls:Forcing a single rule on the entire list. Always consider interleaving when differences appear inconsistent. Final Answer:20

Question 15

Number series (primes): 11, 13, 17, 19, 23, 29, 31, 37, 41, (…) Identify the next term that correctly continues this prime-number sequence.

Accepted Answer

Introduction / Context:This question tests recognition of prime-number sequences in quantitative aptitude. Primes are integers greater than 1 with exactly two positive divisors: 1 and the number itself. Spotting primes and continuing a prime sequence is a foundational skill for many number series problems. Given Data / Assumptions: Sequence provided: 11, 13, 17, 19, 23, 29, 31, 37, 41. Terms are strictly increasing and appear to be consecutive primes in ascending order. We must find the next prime after 41. Concept / Approach:To extend a prime sequence, test successive integers after the last term for primality (no divisors other than 1 and itself). Typical quick checks include divisibility by small primes (2, 3, 5, 7). Step-by-Step Solution: The last given prime is 41.Check 42: divisible by 2 and 3, so not prime.Check 43: not divisible by 2 (odd), by 3 (4+3=7, not multiple of 3), by 5 (does not end in 0 or 5), or by 7 (43 / 7 is not an integer). 43 is prime.Therefore, the next consecutive prime after 41 is 43. Verification / Alternative check:List known consecutive primes around 40: 37, 41, 43, 47. The next after 41 is indeed 43. Why Other Options Are Wrong: 47, 53: These are primes but not the immediate next prime. 51: Composite (51 = 3 * 17). Common Pitfalls:Confusing “any prime” with “next prime.” Always ensure immediacy in ordered prime sequences. Final Answer:43

Question 16

Number series (alternate ×3 and ÷2 pattern): 8, 24, 12, 36, 18, 54, (…) Find the next term that correctly continues the alternating multiplication/division sequence.

Accepted Answer

Introduction / Context:Many number series use alternating operations. Recognizing the repeating pattern (multiply by a constant, then divide by a constant) allows quick continuation of the sequence. Given Data / Assumptions: Given terms: 8, 24, 12, 36, 18, 54, (…) We suspect an alternating rule between consecutive terms. Concept / Approach:Compare each transition: 8 to 24 appears as ×3, then 24 to 12 as ÷2. If this alternates, the pattern is ×3, ÷2, ×3, ÷2, and so on. Step-by-Step Solution: 8 × 3 = 24.24 ÷ 2 = 12.12 × 3 = 36.36 ÷ 2 = 18.18 × 3 = 54.Next operation should be ÷2: 54 ÷ 2 = 27. Verification / Alternative check:Continue one more step mentally to ensure consistency: after 27, the next would be ×3 → 81, reinforcing the alternating structure. Why Other Options Are Wrong: 108 and 72: These would match a ×2 or ×4 step, which breaks the ÷2 requirement at this position. 68: Does not match any simple consistent factor with the pattern. Common Pitfalls:Applying the wrong operation order (e.g., dividing when multiplication is due). Always map the full alternating pattern before computing the next term. Final Answer:27

Question 17

Number series (increasing differences by 2): 2, 6, 12, 20, 30, 42, 56, (…) Determine the next term by analyzing the second-order pattern in differences.

Accepted Answer

Introduction / Context:This sequence grows faster than linear, suggesting a pattern in the differences. Many aptitude series increase the gap between terms by a constant increment (here, by 2). Given Data / Assumptions: Terms: 2, 6, 12, 20, 30, 42, 56, (…) We consider first differences to detect a secondary pattern. Concept / Approach:Compute consecutive differences and inspect whether those differences follow a simple rule (e.g., arithmetic progression). If the differences increase by 2 each time, we can extrapolate the next difference. Step-by-Step Solution: 6 − 2 = 4.12 − 6 = 6.20 − 12 = 8.30 − 20 = 10.42 − 30 = 12.56 − 42 = 14.Differences are 4, 6, 8, 10, 12, 14 (an arithmetic sequence with common difference 2).Next difference = 16; therefore next term = 56 + 16 = 72. Verification / Alternative check:Check the pattern against earlier terms: each step adds consecutive even numbers starting from 4; this holds throughout. Why Other Options Are Wrong: 61, 64, 70: Do not match adding 16 to 56; they would imply incorrect next differences. Common Pitfalls:Assuming multiplication when addition with changing differences is used. Always examine differences before products or ratios. Final Answer:72

Question 18

Number series (alternating signs, doubling magnitude): 4, -8, 16, -32, 64, (…) Find the next term that preserves the alternating sign and geometric growth.

Accepted Answer

Introduction / Context:This is a classic alternating-sign geometric sequence. The absolute value doubles each step, while the sign flips positive/negative alternately. Given Data / Assumptions: Terms: 4, -8, 16, -32, 64, (…) Common ratio in magnitude appears to be 2. Signs alternate +, −, +, −, +, … Concept / Approach:A geometric pattern with consistent doubling implies next magnitude is previous magnitude * 2. The sign alternates each term, so follow the established sign order. Step-by-Step Solution: |4| → |−8|: 4 * 2 = 8 (sign flips to negative).|−8| → |16|: 8 * 2 = 16 (sign flips to positive).|16| → |−32|: 16 * 2 = 32 (sign flips to negative).|−32| → |64|: 32 * 2 = 64 (sign flips to positive).Next: 64 * 2 = 128 with sign flipping to negative → −128. Verification / Alternative check:Express as term n: a1 = 4, a(n) = 4 * 2^(n−1) with sign (−1)^(n−1). For n = 6, a6 = −128, which matches. Why Other Options Are Wrong: 128: Correct magnitude but wrong sign. 192, −192: Do not fit doubling; they imply ×3. Common Pitfalls:Forgetting to alternate signs while applying the geometric factor. Track both magnitude and sign positions. Final Answer:-128

Question 19

Number series (n^3 − 1 pattern): 7, 26, 63, 124, 215, 342, (…) Identify the next term generated by the cubic-minus-one rule.

Accepted Answer

Introduction / Context:Some sequences are built from polynomial expressions of n. Here the terms closely match cubes minus one, a common pattern in competitive quantitative questions. Given Data / Assumptions: Observed terms: 7, 26, 63, 124, 215, 342. Test whether each term equals k^3 − 1 for successive integers k. Concept / Approach:Compute small cubes and subtract 1: 2^3 − 1 = 7, 3^3 − 1 = 26, 4^3 − 1 = 63, and so on. If this fits all given terms, continue with the next integer. Step-by-Step Solution: 2^3 − 1 = 8 − 1 = 7 ✔3^3 − 1 = 27 − 1 = 26 ✔4^3 − 1 = 64 − 1 = 63 ✔5^3 − 1 = 125 − 1 = 124 ✔6^3 − 1 = 216 − 1 = 215 ✔7^3 − 1 = 343 − 1 = 342 ✔Next term: 8^3 − 1 = 512 − 1 = 511. Verification / Alternative check:Confirm monotonic growth matching cubic trend; differences rise consistently, as expected for polynomial sequences. Why Other Options Are Wrong: 481, 391, 421: Do not equal any (n^3 − 1) for n ∈ N after 7. Common Pitfalls:Assuming arithmetic or geometric progressions; always test simple power-based constructions (squares, cubes) when numbers align closely with known powers. Final Answer:511

Question 20

Number series (alternating *2 and +3): 5, 10, 13, 26, 29, 58, 61, (…) Find the next term by following the repeat pattern of operations.

Accepted Answer

Introduction / Context:Alternating-operation series are common: the same two steps repeat—typically a multiplication followed by an addition. Recognizing this cycle quickly yields the next term. Given Data / Assumptions: Series: 5, 10, 13, 26, 29, 58, 61, (…) Observe pairing of operations between successive terms. Concept / Approach:Identify a repeating pattern: ×2 then +3. Validate across all transitions, then apply to compute the next term. Step-by-Step Solution: 5 × 2 = 10.10 + 3 = 13.13 × 2 = 26.26 + 3 = 29.29 × 2 = 58.58 + 3 = 61.Next operation is ×2: 61 × 2 = 122. Verification / Alternative check:Continue one more hypothetical step: 122 + 3 = 125 would be the following term, confirming the cycle consistency. Why Other Options Are Wrong: 64, 125, 128: These correspond to misapplied steps (+3 at the wrong time or different multipliers). Common Pitfalls:Applying +3 twice in a row or reversing the order. Always mark the positions of operations to avoid a mismatch. Final Answer:122

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