Question 1

Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?

Accepted Answer

Given data Series: 2, 1, (1/2), (1/4), ... Concept/Approach The terms are halved each time (multiply by (1/2)). Step-by-Step calculation 2 → 1 (multiply by (1/2))1 → (1/2) (multiply by (1/2))(1/2) → (1/4) (multiply by (1/2))Next: (1/4) × (1/2) = (1/8) Verification/Alternative General term an = 2 × (1/2)n-1. For n = 4, a4 = 2×(1/8) = (1/4); for n = 5, a5 = (1/8). Common pitfalls Using subtraction instead of a ratio pattern. Final Answer (1/8)

Question 2

Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

Accepted Answer

Given data Series: 7, 10, 8, 11, 9, 12, ... Concept/Approach Two interleaved sequences: Odd positions: 7, 8, 9, ... (increase by 1) Even positions: 10, 11, 12, ... (increase by 1) Step-by-Step calculation Positions 1–6 given → next is position 7 (odd subsequence): 7, 8, 9, 10 ... Verification/Alternative Pattern holds if we list pairs: (7,10), (8,11), (9,12), next pair starts with 10. Common pitfalls Adding 3 then subtracting 2 alternately; that fails at later terms. Final Answer 10

Question 3

Look at this series: 36, 34, 30, 28, 24, ... What number should come next?

Accepted Answer

Given data Series: 36, 34, 30, 28, 24, ... Concept/Approach Alternating differences: −2, −4, −2, −4, ... Step-by-Step calculation 36 − 2 = 3434 − 4 = 3030 − 2 = 2828 − 4 = 24Next: 24 − 2 = 22 Verification/Alternative Differences repeat in a 2-step cycle (−2, −4), so the next must be −2. Common pitfalls Continuing with −4 again; that would break the alternation. Final Answer 22

Question 4

Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?

Accepted Answer

Given data Series: 22, 21, 23, 22, 24, 23, ... Concept/Approach Alternating pattern: −1, +2, −1, +2, −1, +2, ... Step-by-Step calculation 22 − 1 = 2121 + 2 = 2323 − 1 = 2222 + 2 = 2424 − 1 = 23Next: 23 + 2 = 25 Verification/Alternative Check two-step cycle repeats consistently. Common pitfalls Assuming constant difference (+1 or −1) which does not fit all terms. Final Answer 25

Question 5

Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?

Accepted Answer

Given data Series: 53, 53, 40, 40, 27, 27, ... Concept/Approach Numbers repeat in pairs; every new pair starts 13 less than the previous pair's value. Step-by-Step calculation 53, 53 → 40, 40 (53 − 13)40, 40 → 27, 27 (40 − 13)Next pair value = 27 − 13 = 14 → next term 14 Verification/Alternative Pattern is: a, a, a−13, a−13, a−26, a−26, ... Common pitfalls Subtracting 13 from each term without noticing the pair repetition. Final Answer 14

Question 6

Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?

Accepted Answer

Given data Series: 21, 9, 21, 11, 21, 13, 21, ... Concept/Approach Alternating constant 21 with an increasing odd sequence (9, 11, 13, 15, ...). Step-by-Step calculation After 21, the odd numbers go 9 → 11 → 13 → next 15So the next term following 21 is 15 Verification/Alternative Two interleaved sequences: positions odd = 21; positions even = 9, 11, 13, 15, ... Common pitfalls Expecting a single arithmetic progression. Final Answer 15

Question 7

Look at this series: 58, 52, 46, 40, 34, ... What number should come next?

Accepted Answer

Given data Series: 58, 52, 46, 40, 34, ... Concept/Approach Simple arithmetic progression with common difference −6. Step-by-Step calculation 58 − 6 = 5252 − 6 = 4646 − 6 = 4040 − 6 = 34Next: 34 − 6 = 28 Verification/Alternative Constant difference check = −6 for all steps. Common pitfalls Switching to a different difference mid-way. Final Answer 28

Question 8

Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?

Accepted Answer

Given data Series: 3, 4, 7, 8, 11, 12, ... Concept/Approach Alternating increments: +1, +3, +1, +3, +1, ... Step-by-Step calculation 3 + 1 = 44 + 3 = 77 + 1 = 88 + 3 = 1111 + 1 = 12Next: 12 + 3 = 15 Verification/Alternative View as two interleaved sequences of increments repeating every two steps. Common pitfalls Assuming +2 repeating; that fails at 7 → 8. Final Answer 15

Question 9

Look at this series: 8, 22, 8, 28, 8, ... What number should come next?

Accepted Answer

Given data Series: 8, 22, 8, 28, 8, ... Concept/Approach Alternating constant and increasing terms: every other term is 8; the alternating terms increase by 6. Step-by-Step calculation Non-8 subsequence: 22 → 28 → next 34 (add 6)So the next term is 34 Verification/Alternative Positions: 1=8, 2=22, 3=8, 4=28, 5=8, 6=34. Common pitfalls Adding 6 to the 8 instead of only to the alternating large terms. Final Answer 34

Question 10

Look at this series: 31, 29, 24, 22, 17, ... What number should come next?

Accepted Answer

Given data Series: 31, 29, 24, 22, 17, ... Concept/Approach Alternating differences: −2, −5, −2, −5, ... Step-by-Step calculation 31 − 2 = 2929 − 5 = 2424 − 2 = 2222 − 5 = 17Next: 17 − 2 = 15 Verification/Alternative Two-step cycle (−2, −5) repeats, so the next subtraction is −2. Common pitfalls Subtracting another 5, which would break the pattern. Final Answer 15

Question 11

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?

Accepted Answer

Given data Series terms: 1.5, 2.3, 3.1, 3.9, ... Concept/Approach Check consecutive differences to spot a constant step. Step-by-step calculation 2.3 − 1.5 = 0.83.1 − 2.3 = 0.83.9 − 3.1 = 0.8Next term = 3.9 + 0.8 = 4.7 Verification/Alternative A simple arithmetic progression with common difference 0.8 fits all terms. Common pitfalls Assuming alternating steps (they are constant here). Final Answer 4.7

Question 12

Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?

Accepted Answer

Given data Sequence: 14, 28, 20, 40, 32, 64, ... Concept/Approach Two-step repeating pattern: multiply by 2, then subtract 8. Step-by-step calculation 14 × 2 = 2828 − 8 = 2020 × 2 = 4040 − 8 = 3232 × 2 = 64Next: 64 − 8 = 56 Verification/Alternative Odd-index terms are doubled to get the next, then 8 is subtracted to get the following term. Common pitfalls Continuing to double after 64 and ignoring the alternating subtraction. Final Answer 56

Question 13

Look at this series: 2, 4, 6, 8, 10, ... What number should come next?

Accepted Answer

Given data Even-number sequence: 2, 4, 6, 8, 10, ... Concept/Approach Arithmetic progression with common difference 2. Step-by-step calculation Next = 10 + 2 = 12 Verification/Alternative General term 2n gives 10 = 2×5, so the next is 2×6 = 12. Common pitfalls Choosing an odd number; all terms are even. Final Answer 12

Question 14

Look at this series: 201, 202, 204, 207, ... What number should come next?

Accepted Answer

Given data Sequence: 201, 202, 204, 207, ... Concept/Approach Successive increments increase by 1: +1, +2, +3, ... Step-by-step calculation 201 + 1 = 202202 + 2 = 204204 + 3 = 207Next: 207 + 4 = 211 Verification/Alternative Pattern of triangular increments holds across terms. Common pitfalls Adding a constant step instead of increasing steps. Final Answer 211

Question 15

Look at this series: 544, 509, 474, 439, ... What number should come next?

Accepted Answer

Given data Sequence: 544, 509, 474, 439, ... Concept/Approach Constant decrement sequence. Step-by-step calculation 544 − 509 = 35509 − 474 = 35474 − 439 = 35Next = 439 − 35 = 404 Verification/Alternative All differences equal −35, so the pattern is consistent. Common pitfalls Mis-subtracting the 35 difference. Final Answer 404

Question 16

Look at this series: 80, 10, 70, 15, 60, ... What number should come next?

Accepted Answer

Given data Sequence: 80, 10, 70, 15, 60, ... Concept/Approach Two interleaved patterns: first, numbers decreasing by 10; second, numbers increasing by 5. Step-by-step calculation First subsequence (positions 1,3,5,...): 80 → 70 → 60 → (next 50)Second subsequence (positions 2,4,6,...): 10 → 15 → (next 20)Next overall term corresponds to the second subsequence: 20 Verification/Alternative Listing pairs: (80,10), (70,15), (60,20), ... confirms the pattern. Common pitfalls Continuing with 50 immediately; that would be the term after next. Final Answer 20

Question 17

Look at this series: 2, 6, 18, 54, ... What number should come next?

Accepted Answer

Given data Sequence: 2, 6, 18, 54, ... Concept/Approach Geometric progression with common ratio 3. Step-by-step calculation Each step × 3: 2 → 6 → 18 → 54Next = 54 × 3 = 162 Verification/Alternative General term an = 2 × 3n−1; for n = 5, value is 162. Common pitfalls Doubling instead of tripling. Final Answer 162

Question 18

Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?

Accepted Answer

Given data Sequence: 5.2, 4.8, 4.4, 4.0, ... Concept/Approach Constant decrement by 0.4. Step-by-step calculation 5.2 − 0.4 = 4.84.8 − 0.4 = 4.44.4 − 0.4 = 4.0Next = 4.0 − 0.4 = 3.6 Verification/Alternative All steps reduce by the same decimal amount (0.4). Common pitfalls Subtracting 0.2 instead of 0.4 due to decimal oversight. Final Answer 3.6

Question 19

Look at this series: 8, 6, 9, 23, 87, ... What number should come next?

Accepted Answer

Given data Terms: 8, 6, 9, 23, 87, ... Concept/Approach The recursive rule follows an increasing multiplier with a concurrent linear subtraction: multiply by n and subtract (n + 1), where n starts at 1 for the move from the first term. Step-by-step calculation 8 × 1 − 2 = 66 × 2 − 3 = 99 × 3 − 4 = 2323 × 4 − 5 = 87Next uses n = 5: 87 × 5 − 6 = 435 − 6 = 429 Verification/Alternative The pattern '×n then −(n+1)' consistently reproduces every given transition; extending it yields 429. Common pitfalls Searching for fixed differences or ratios; neither is constant here. Assuming alternating add/subtract without the multiplicative growth. Final Answer 429

Question 20

Number series – find the next two terms: 28, 25, 5, 21, 18, 5, 14, ?, ?

Accepted Answer

Introduction / Context: This sequence mixes a small constant decrement with two alternating adjustments whose magnitudes reduce in a steady pattern. We must project the rule two more steps to find the next pair. Given Data / Assumptions: Series (spaces imply commas): 28, 25, 5, 21, 18, 5, 14, ?, ? We want terms 8 and 9. Observed differences: -3, -20, +16, -3, -13, +9, -3, … Concept / Approach: Notice a repeating three-step motif: subtract 3, subtract a larger value, then add a value. The larger subtraction and the addition each decrease by 7 on successive cycles. Step-by-Step Solution: Cycle 1: 28 → 25 (−3), 25 → 5 (−20), 5 → 21 (+16)Cycle 2: 21 → 18 (−3), 18 → 5 (−13), 5 → 14 (+9)Next cycle decrements: −3, then −6 (since 20 → 13 → 6 decreases by 7), then +2 (since 16 → 9 → 2 also decreases by 7).Apply −3 to 14: 14 − 3 = 11.Apply −6 next: 11 − 6 = 5. Verification / Alternative check: Projecting further with +2 would give 7, consistent with the established 16 → 9 → 2 trend in the additive leg. Why Other Options Are Wrong: 10 7, 11 8, 5 10, 10 5 do not align with the strictly “−3, then (−7 less than previous large subtraction), then (+7 less than previous addition)” pattern. Common Pitfalls: Assuming a single arithmetic progression or alternating parity sequences fails because the sequence uses a three-step cyclic difference pattern. Final Answer: 11 5

Number Series Questions