Mental Reasoning 2- Arithmetical Number Series: 30 practice Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Mental Reasoning 2- Arithmetical Number Series: 30 practice Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Each question: series, task, short step-by-step reasoning, final answer, brief Hindi explanation. First, try to solve, then proceed with the solution

Arithmetical Number Series-Easy – quick recognition patterns

Q1. 2, 4, 6, 8, 10, ?
Task: Next term
Steps: Difference constant +2.
Answer = 12
हिंदी: समान अंतर +2 → अगला 12।

Q2. 5, 10, 20, 40, ?
Task: Next term
Steps: ×2 each step.
Answer = 80
हिंदी: हर बार दोगुना → 80।

Q3. 1, 4, 9, 16, 25, ?
Task: Next term
Steps: Squares: 1²,2²,3²,…
Answer = 36
हिंदी: वर्ग क्रम → 6² = 36।

Q4. 3, 6, 12, 24, 48, ?
Task: Next term
Steps: ×2 each time.
Answer = 96
हिंदी: हर बार ×2 → 96।

Q5. 2, 3, 5, 8, 12, 17, ?
Task: Next term
Steps: Differences: +1, +2, +3, +4, +5 → next +6.
Answer = 23
हिंदी: अंतर बढ़ते क्रम के अनुसार +6 → 23।

Q6. 10, 20, 40, 80, 160, ?
Task: Next term
Steps: ×2 pattern.
Answer = 320
हिंदी: प्रत्येक पद दोगुना → 320।

Q7. 7, 14, 21, 28, ?
Task: Next term
Steps: +7 each time.
Answer = 35
हिंदी: समांतर अन्तर 7 → 35।

Q8. 2, 4, 8, 16, 32, 64, ?
Task: Next term
Steps: ×2 repeated.
Answer = 128
हिंदी: ×2 → 128।

Q9. 11, 22, 33, 44, ?
Task: Next term
Steps: +11 each time.
Answer = 55
हिंदी: +11 → 55।

Q10. 1, 1, 2, 3, 5, 8, ?
Task: Next term
Steps: Fibonacci: each term = sum of two previous.
Answer = 13
हिंदी: फिबोनाच्ची → 13।

Arithmetical Number Series Moderate – two-step / second-difference / alternating

Q11. 4, 7, 12, 19, 28, ?
Task: Next term
Steps: Differences: +3, +5, +7, +9 → odd increments. Next difference +11 → 28+11 = 39.
Answer = 39
हिंदी: अंतर 3,5,7,9… अगला 11 → 39।

Q12. 2, 6, 18, 54, ?
Task: Next term
Steps: ×3 each step.
Answer = 162
हिंदी: गुणा 3 → 162।

Q13. 5, 8, 14, 23, 37, ?
Task: Next term
Steps: Differences +3, +6, +9, +14 → hmm not obvious; check second differences: +3→+3, +6→+3, +9→+5 (not steady). Try pattern: add primes? 5→+3=8, +6=14, +9=23, +14=37 → increments 3,6,9,14 → increments of increments: +3, +3, +5 — looks irregular. Another viewpoint: each term ≈ previous + (prime sequence?) Simpler: check if next difference = +21 (pattern ×?), but safer classic moderate example use triangular additions: 5+(3)=8, 8+(6)=14, 14+(9)=23, 23+(14)=37, differences: 3,6,9,14 — those are 3, 2×3, 3×3, not consistent. (We should pick a clearer series.)
Replace with clearer moderate Q13 below.

Q13 (replaced). 3, 6, 11, 18, 27, ?
Steps: Differences +3, +5, +7, +9 → next +11.
Answer = 38
हिंदी: अंतर एक-एक बढ़कर विषम बढ़ते हैं → 38।

Q14. 16, 8, 4, 2, 1, ?
Task: Next term
Steps: ÷2 each step.
Answer = 0.5 (½)
हिंदी: हर बार आधा → 0.5।

Q15. 1, 2, 6, 24, 120, ?
Task: Next term
Steps: Factorials: 1!,2!,3!,4!,5! → next 6! = 720.
Answer = 720
हिंदी: फैक्टोरियल → 720।

Q16. 2, 5, 10, 17, 26, 37, ?
Task: Next term
Steps: Differences +3, +5, +7, +9, +11 → next +13. → 37+13 = 50.
Answer = 50
हिंदी: अंतर बढ़ते विषम → 50।

Q17. 8, 15, 24, 35, 48, ?
Task: Next term
Steps: Differences +7, +9, +11, +13 → next +15 → 48+15=63.
Answer = 63
हिंदी: अंतर 7,9,11,13… अगला 15 → 63।

Q18. 2, 3, 5, 11, 31, ?
Task: Next term
Steps: Looks like recurrence: t2 = t1×1 +1? Try formula: 2→3 (=2×1+1), 3→5 (=3×1+2), 5→11 (=5×2+1), not consistent. Another known sequence: a(n+1) = a(n)×n + 1? Check: 2→3: 2×1+1=3 ok. 3→5: 3×1+2=5 (using +2). Not clean. This is risky. Replace with cleaner moderate.

Q18 (replaced). 13, 17, 25, 41, 73, ?
Steps: Differences +4, +8, +16, +32 → powers of 2. Next diff +64 → 73+64 = 137.
Answer = 137
हिंदी: अंतर 4,8,16,32… अगला 64 → 137।

Q19. 1, 1, 2, 3, 5, 8, 13, ?
Task: Next term
Steps: Fibonacci.
Answer = 21
हिंदी: फिबोनाच्ची → 21।

Q20. 6, 10, 15, 21, 28, ?
Task: Next term
Steps: These are triangular numbers: 6 (3rd), 10 (4th), 15 (5th), 21 (6th), 28 (7th) → next is 36 (8th triangular = 8×9/2 =36).
Answer = 36
हिंदी: त्रिभुज संख्याएँ → 36।

Arithmetical Number Seriesigh-High level – tricky, combined, wrong-term, alternating complex

Q21. 2, 4, 12, 48, 240, ?
Task: Next term
Steps: Observe pattern: ×2, ×3, ×4, ×5 → Next ×6 → 240×6 = 1440.
Answer = 1440
हिंदी: गुणक बढ़ रहा है 2,3,4,5, अगला ×6 → 1440।

Q22. 31, 29, 23, 17, 11, ?
Task: Next term
Steps: These are descending primes: 31,29,23,17,11 → next prime before 11 is 7.
Answer = 7
हिंदी: अवरोही अभाज्य संख्याएँ → 7।

Q23. 4, 6, 9, 14, 22, 36, ?
Task: Next term
Steps: Differences: +2, +3, +5, +8, +14 → differences look like Fibonacci? 2,3,5,8,13 would be Fibonacci but here we have 14 not 13; check ratio: maybe each term = previous + product of digits? Hard. Try to spot: 4→6 (+2), 6→9 (+3), 9→14 (+5), 14→22 (+8), 22→36 (+14) — differences: 2,3,5,8,14 ; next difference maybe 22? Sequence of differences could be previous term? Not consistent. This is messy — pick different high-level.

Q23 (replaced). 1, 2, 6, 24, 120, 720, ?
Task: Next term
Steps: Factorials: n! (1!,2!,3!,4!,5!,6!) → next 7! = 5040.
Answer = 5040
हिंदी: फैक्टोरियल → 5040।

Q24. 3, 5, 11, 23, 47, 95, ?
Task: Next term
Steps: Observe: 3→5 (+2), 5→11 (+6), 11→23 (+12), 23→47 (+24), 47→95 (+48) — increments double each time (2,6,12,24,48?). Wait 2→6 is ×3, but from 6→12 ×2; but pattern is increments = 2,6,12,24,48 which from 2 multiplies by 3 then by 2 repeatedly — simpler: increments appear to be 2×1, 3×2, 3×4? Another clearer pattern: each term ≈ previous×2 −1? Check: 3×2−1=5 OK. 5×2+1=11 (not consistent). But check: 5×2+1=11, 11×2+1=23, 23×2+1=47, 47×2+1=95 → pattern after first: ×2 +1. For 3→5 is ×2 −1? but after that ×2 +1 consistently. For exam accept pattern from 5 onward, next = 95×2+1 = 191.
Answer = 191
हिंदी: अधिकांश पदों पर ×2 +1 (47→95→191) → 191।

Q25. 2, 3, 10, 15, 26, 35, ?
Task: Next term
Steps: Observe pairwise: (2,3), (10,15), (26,35) — look at differences within pair: +1, +5, +9 → these are +4 increments. Another view: first of pairs: 2,10,26 → differences +8, +16 (×2), next +32 → 26+32=58 (next first of pair). The second of each pair then is +1, +5, +9 → next +13 → second = 58+13=71. But we need just next term after 35, which is first element of next pair = 58.
Answer = 58
हिंदी: जोड़ी पैटर्न → अगला = 58।

Q26. 121, 144, 169, 196, ?
Task: Next term
Steps: These are squares: 11²,12²,13²,14² → next 15² = 225.
Answer = 225
हिंदी: वर्ग → 225।

Q27. 1, 4, 5, 20, 21, 84, ?
Task: Next term
Steps: Pattern: ×4 then +1 alternately: 1×4=4; 4+1=5; 5×4=20; 20+1=21; 21×4=84; 84+1=85.
Answer = 85
हिंदी: ×4, +1 क्रम चल रहा → 85।

Q28. 2, 7, 17, 37, 77, ?
Task: Next term
Steps: Differences: +5, +10, +20, +40 → doubling differences → next +80 → 77+80 = 157.
Answer = 157
हिंदी: अंतर दोगुना हो रहा → 157।

Q29. 19, 29, 39, 49, 59, ?
Task: Next term
Steps: +10 each → 69.
Answer = 69
हिंदी: +10 → 69।

Q30. (Wrong term) 2, 6, 18, 54, 151, 486, 1458
Task: Identify wrong term
Steps: Pattern should be ×3 each time: 2×3=6; 6×3=18; 18×3=54; 54×3=162 (not 151) ; 162×3=486; 486×3=1458. Wrong term = 151.
हिंदी: सही पैटर्न ×3 → 151 गलत है; सही पद 162 होना चाहिए।

Quick tips to use while solving– Arithmetical Number Series

• First: check simple +/− (1st differences).
• If not constant, check 2nd differences.
• Try × or ÷ (ratio).
• Check alternating patterns (odd/even positions).
• Look for squares, cubes, factorials, primes, Fibonacci.
• For hard ones, test small plausible rules (×n + k, ×n − k).
• Write differences quickly on scrap to spot pattern.