1001, 8001, 27001, 64001, 125001,…
Answer: B
Correct answer: 216001
Each term is a cube multiplied by a thousand, plus one: \( 1000\cdot1+1 \), \( 1000\cdot8+1 \), \( 1000\cdot27+1 \), \( 1000\cdot64+1 \), \( 1000\cdot125+1 \), so the next is \( 1000 \times 216 + 1 = \mathbf{216001} \).
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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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999, 7999, 26999, 63999,….
Answer: B
Correct answer: 124999
Each term is a cube multiplied by a thousand, less one: \( 1000-1 \), \( 8000-1 \), \( 27000-1 \), \( 64000-1 \), so the next is \( 125000 - 1 = \mathbf{124999} \).
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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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1010, 8020, 27030, 64040,….
Answer: B
Correct answer: 125050
Each term is a cube times a thousand, plus ten times its root: \( 1000+10 \), \( 8000+20 \), \( 27000+30 \), \( 64000+40 \), so the next is \( 125000 + 50 = \mathbf{125050} \).
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0, 6, 24, 60,…. 210
Answer: D
Correct answer: 120
Each term is a cube less its own root: \( 1^3-1=0 \), \( 2^3-2=6 \), \( 3^3-3=24 \), \( 4^3-4=60 \), so the next is \( 5^3-5 = \mathbf{120} \), followed by \( 6^3-6 = 210 \).
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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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Which number would replace the question mark (?) in the series 2, 7, 14, 23, ?, 47
Answer: B
Correct answer: 34
The gaps are the successive odd numbers: \( 7-2=5 \), \( 14-7=7 \), \( 23-14=9 \). The next gap is 11, giving \[ 23 + 11 = \mathbf{34} \] and \( 34 + 13 = 47 \), as shown.
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Which is the number that should come next in the following series? 4, 6, 12, 14, 28, 30, --
Answer: D
The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... Clearly the number to be found belongs to the first series. Now the pattern followed is +8, +16, +32. So, missing number = (28 + 32) = 60 Hence the answer is (4)
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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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