11, 13, 17, 19, 23, 29, 31, 37, 41, --
Answer: A
Correct answer: 43
The terms are the prime numbers in order, from 11 to 41, so the next prime is 43. 51 is \( 3\times17 \) and so not prime.
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4, 9, 13, 22, 35, --
Answer: A
Correct answer: 57
Each term is the sum of the two before it: \( 4+9=13 \), \( 9+13=22 \), \( 13+22=35 \), so the next is \[ 22 + 35 = \mathbf{57} \]
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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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2, 10, 30, 68,….222
Answer: A
Correct answer: 130
Each term is a cube plus its own root: \( 1^3+1=2 \), \( 2^3+2=10 \), \( 3^3+3=30 \), \( 4^3+4=68 \), so the next is \( 5^3+5 = \mathbf{130} \), followed by \( 6^3+6 = 222 \).
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0, 7, 26, 63, 124,…
Answer: D
Correct answer: 215
Each term is one less than a cube: \( 1^3-1=0 \), \( 2^3-1=7 \), \( 3^3-1=26 \), \( 4^3-1=63 \), \( 5^3-1=124 \), so the next is \( 6^3-1 = \mathbf{215} \).
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4, 16, 36, 64, …. 144
Answer: C
Correct answer: 100
The terms are the squares of the even numbers: \( 2^2=4 \), \( 4^2=16 \), \( 6^2=36 \), \( 8^2=64 \), so the next is \( 10^2 = \mathbf{100} \), followed by \( 12^2 = 144 \).
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3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?
Answer: B
The given sequence is a combination of two series :
I. 3, 7, 13, 21, 31, ? and II. 4, 7, 13, 22, 34
The pattern in I is + 4, + 6, + 8, + 10,.....
The pattern in II is + 3, + 6, + 9, + 12,.....
So, missing term = 31 + 12 = 43.
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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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Find the wrong number in the series. 7, 28, 63, 124, 215, 342
Answer: B
Correct answer: 28
Each term should be one less than a cube: \( 2^3-1=7 \), \( 3^3-1=26 \), \( 4^3-1=63 \), \( 5^3-1=124 \), \( 6^3-1=215 \), \( 7^3-1=342 \). The second term is given as 28 where it should be 26, so that is the wrong one.
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990, 7980, 26970, 63960,….
Answer: D
Correct answer: 124950
Each term is a cube times a thousand, less ten times its root: \( 1000-10 \), \( 8000-20 \), \( 27000-30 \), \( 64000-40 \), so the next is \( 125000 - 50 = \mathbf{124950} \).
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