This lesson shows how to find the rule, then gives each pattern with the reason it works. It solves five examples step by step and lists the traps that cost marks.
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Q1. Find the wrong number in the series: 31, 38, 35, 43, 39, 47, 43
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Answer: D
This series alternates: add 8, then subtract 4, and repeat. Check each step: 31 to 38 is +7 (should be +8), 38 to 35 is -3 (should be -4), 35 to 43 is +8 (OK), 43 to 39 is -4 (OK), 39 to 47 is +8 (OK), 47 to 43 is -4 (OK). One or more steps near 38 break this pattern. So 38 is the wrong number.
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Q2. Find the next number in the series: 343, 512, 729, 1000, ?
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Answer: A
This series lists consecutive perfect cubes, starting from 7^3. Check each term: 7^3=343, 8^3=512, 9^3=729, 10^3=1000. Following this pattern, the next base number is 11. So the next term is 11^3=1331.
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Q3. Find the next number in the series: 125, 216, 343, 512, ?
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Answer: B
This series lists consecutive perfect cubes, starting from 5^3. Check each term: 5^3=125, 6^3=216, 7^3=343, 8^3=512. Following this pattern, the next base number is 9. So the next term is 9^3=729.
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Q4. Find the next number in the series: 1, 8, 27, 64, ?
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Answer: C
This series lists consecutive perfect cubes, starting from 1^3. Check each term: 1^3=1, 2^3=8, 3^3=27, 4^3=64. Following this pattern, the next base number is 5. So the next term is 5^3=125.
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Q5. Find the next number in the series: 27, 64, 125, 216, ?
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Answer: D
This series lists consecutive perfect cubes, starting from 3^3. Check each term: 3^3=27, 4^3=64, 5^3=125, 6^3=216. Following this pattern, the next base number is 7. So the next term is 7^3=343.
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Q6. Find the next number in the series: 512, 729, 1000, 1331, ?
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Answer: A
This series lists consecutive perfect cubes, starting from 8^3. Check each term: 8^3=512, 9^3=729, 10^3=1000, 11^3=1331. Following this pattern, the next base number is 12. So the next term is 12^3=1728.
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Q7. Find the next number in the series: 64, 125, 216, 343, ?
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Answer: B
This series lists consecutive perfect cubes, starting from 4^3. Check each term: 4^3=64, 5^3=125, 6^3=216, 7^3=343. Following this pattern, the next base number is 8. So the next term is 8^3=512.
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Q8. Find the next number in the series: 8, 27, 64, 125, ?
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Answer: B
This series lists consecutive perfect cubes, starting from 2^3. Check each term: 2^3=8, 3^3=27, 4^3=64, 5^3=125. Following this pattern, the next base number is 6. So the next term is 6^3=216.
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Q9. Find the next number in the series: 216, 343, 512, 729, ?
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Answer: A
This series lists consecutive perfect cubes, starting from 6^3. Check each term: 6^3=216, 7^3=343, 8^3=512, 9^3=729. Following this pattern, the next base number is 10. So the next term is 10^3=1000.
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Q10. Find the next number in the series: 64, 81, 100, 121, 144, ?
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Answer: C
This series lists consecutive perfect squares, starting from 8^2. Check each term: 8^2=64, 9^2=81, 10^2=100, 11^2=121, 12^2=144. Following this pattern, the next base number is 13. So the next term is 13^2=169.
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Q11. Find the next number in the series: 81, 100, 121, 144, 169, ?
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Answer: D
This series lists consecutive perfect squares, starting from 9^2. Check each term: 9^2=81, 10^2=100, 11^2=121, 12^2=144, 13^2=169. Following this pattern, the next base number is 14. So the next term is 14^2=196.
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Q12. Find the next number in the series: 49, 64, 81, 100, 121, ?
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Answer: C
This series lists consecutive perfect squares, starting from 7^2. Check each term: 7^2=49, 8^2=64, 9^2=81, 10^2=100, 11^2=121. Following this pattern, the next base number is 12. So the next term is 12^2=144.
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Q13. Find the next number in the series: 36, 49, 64, 81, 100, ?
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Answer: A
This series lists consecutive perfect squares, starting from 6^2. Check each term: 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100. Following this pattern, the next base number is 11. So the next term is 11^2=121.
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Q14. Find the next number in the series: 1, 4, 9, 16, 25, ?
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Answer: B
This series lists consecutive perfect squares, starting from 1^2. Check each term: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25. Following this pattern, the next base number is 6. So the next term is 6^2=36.
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Q15. Find the next number in the series: 16, 25, 36, 49, 64, ?
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Answer: D
This series lists consecutive perfect squares, starting from 4^2. Check each term: 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64. Following this pattern, the next base number is 9. So the next term is 9^2=81.
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Q16. Find the next number in the series: 25, 36, 49, 64, 81, ?
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Answer: B
This series lists consecutive perfect squares, starting from 5^2. Check each term: 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81. Following this pattern, the next base number is 10. So the next term is 10^2=100.
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Q17. Find the next number in the series: 4, 9, 16, 25, 36, ?
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Answer: C
This series lists consecutive perfect squares, starting from 2^2. Check each term: 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36. Following this pattern, the next base number is 7. So the next term is 7^2=49.
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Q18. Find the next number in the series: 5, 10, 20, 40, 80, ?
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Answer: A
Each term in this series equals the previous term times 2. Check this rule against the given terms: 5×2=10, 10×2=20, 20×2=40, 40×2=80. The rule holds throughout the series. Apply it once more: 80×2=160. So the next term is 160.
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Q19. Find the next number in the series: 3, 6, 12, 24, 48, ?
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Answer: D
Each term in this series equals the previous term times 2. Check this rule against the given terms: 3×2=6, 6×2=12, 12×2=24, 24×2=48. The rule holds throughout the series. Apply it once more: 48×2=96. So the next term is 96.
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Q20. Find the next number in the series: 2, 6, 18, 54, 162, ?
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Answer: D
Each term in this series equals the previous term times 3. Check this rule against the given terms: 2×3=6, 6×3=18, 18×3=54, 54×3=162. The rule holds throughout the series. Apply it once more: 162×3=486. So the next term is 486.
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Q21. Find the next number in the series: 3, 9, 27, 81, 243, ?
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Answer: A
Each term in this series equals the previous term times 3. Check this rule against the given terms: 3×3=9, 9×3=27, 27×3=81, 81×3=243. The rule holds throughout the series. Apply it once more: 243×3=729. So the next term is 729.
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Q22. Find the next number in the series: 3, 12, 48, 192, 768, ?
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Answer: C
Each term in this series equals the previous term times 4. Check this rule against the given terms: 3×4=12, 12×4=48, 48×4=192, 192×4=768. The rule holds throughout the series. Apply it once more: 768×4=3072. So the next term is 3072.
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Q23. Find the next number in the series: 6, 24, 96, 384, 1536, ?
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Answer: B
Each term in this series equals the previous term times 4. Check this rule against the given terms: 6×4=24, 24×4=96, 96×4=384, 384×4=1536. The rule holds throughout the series. Apply it once more: 1536×4=6144. So the next term is 6144.
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Q24. Find the next number in the series: 4, 8, 16, 32, 64, ?
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Answer: D
Each term in this series equals the previous term times 2. Check this rule against the given terms: 4×2=8, 8×2=16, 16×2=32, 32×2=64. The rule holds throughout the series. Apply it once more: 64×2=128. So the next term is 128.
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Q25. Find the next number in the series: 1, 3, 9, 27, 81, ?
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Answer: A
Each term in this series equals the previous term times 3. Check this rule against the given terms: 1×3=3, 3×3=9, 9×3=27, 27×3=81. The rule holds throughout the series. Apply it once more: 81×3=243. So the next term is 243.
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