101, 401, 901, 1601, 2501, …. 4901
Answer: D
Correct answer: 3601
Each term is a hundred times a square, plus one: \( 100(1)+1=101 \), \( 100(4)+1=401 \), \( 100(9)+1=901 \), \( 100(16)+1=1601 \), \( 100(25)+1=2501 \), so the next is \( 100(36)+1 = \mathbf{3601} \), followed by \( 100(49)+1 = 4901 \).
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3, 8, 15, 24,…48
Answer: D
Correct answer: 35
Each term is one less than a square: \( 2^2-1=3 \), \( 3^2-1=8 \), \( 4^2-1=15 \), \( 5^2-1=24 \), so the next is \( 6^2-1 = \mathbf{35} \), followed by \( 7^2-1 = 48 \).
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99, 80, 63,….35
Answer: B
Correct answer: 48
Each term is one less than a square, counting downwards: \( 10^2-1=99 \), \( 9^2-1=80 \), \( 8^2-1=63 \), so the next is \( 7^2-1 = \mathbf{48} \), followed by \( 6^2-1 = 35 \).
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2, 6, 12, 20, 30,…. 56
Answer: C
Correct answer: 42
Each term is the product of two consecutive numbers: \( 1\cdot2=2 \), \( 2\cdot3=6 \), \( 3\cdot4=12 \), \( 4\cdot5=20 \), \( 5\cdot6=30 \), so the next is \( 6\cdot7 = \mathbf{42} \), followed by \( 7\cdot8 = 56 \).
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110, 132, 156, 182,….
Answer: D
Correct answer: 210
Each term is the product of two consecutive numbers: \( 10\cdot11=110 \), \( 11\cdot12=132 \), \( 12\cdot13=156 \), \( 13\cdot14=182 \), so the next is \( 14\cdot15 = \mathbf{210} \).
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0, 2, 6, 12, 20,….42
Answer: B
Correct answer: 30
Each term is the product of a number and the one below it: \( 1\cdot0=0 \), \( 2\cdot1=2 \), \( 3\cdot2=6 \), \( 4\cdot3=12 \), \( 5\cdot4=20 \), so the next is \( 6\cdot5 = \mathbf{30} \), followed by \( 7\cdot6 = 42 \).
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90, 380, 870, 1560,…..
Answer: B
Correct answer: 2450
Each term is a multiple of ten times the number one less: \( 10\times9=90 \), \( 20\times19=380 \), \( 30\times29=870 \), \( 40\times39=1560 \), so the next is \( 50\times49 = \mathbf{2450} \).
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1, 8, 27, 64,…. 216
Answer: A
Correct answer: 125
The terms are the cubes: \( 1^3, 2^3, 3^3, 4^3 \), so the next is \( 5^3 = \mathbf{125} \), followed by \( 6^3 = 216 \).
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1000, 8000, 27000, 64000,….
Answer: B
Correct answer: 125000
Each term is a cube multiplied by a thousand: \( 1^3, 2^3, 3^3, 4^3 \) times 1000, so the next is \( 5^3 \times 1000 = \mathbf{125000} \).
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2, 9, 28, 65,…217
Answer: D
Correct answer: 126
Each term is one more than a cube: \( 1^3+1=2 \), \( 2^3+1=9 \), \( 3^3+1=28 \), \( 4^3+1=65 \), so the next is \( 5^3+1 = \mathbf{126} \), followed by \( 6^3+1 = 217 \).
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