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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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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15, 31, 63, 127, 255, --
Answer: B
Correct answer: 511
Each term is one less than a power of two: \( 2^4-1=15 \), \( 2^5-1=31 \), \( 2^6-1=63 \), \( 2^7-1=127 \), \( 2^8-1=255 \), so the next is \( 2^9-1 = \mathbf{511} \). Equivalently, each term is twice the one before, plus one.
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5, 11, 17, 25, 33, 43, --
Answer: D
Correct answer: 53
The gaps come in pairs: \( +6, +6 \), then \( +8, +8 \), then \( +10 \) and \( +10 \) again. So after 43 the next term is \[ 43 + 10 = \mathbf{53} \]
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In each of the following questions, one term in the number series is wrong. Find the wrong term
125, 126, 124, 127, 123, 129
Answer: E
Correct answer: 129
The series should add and subtract by turns, the amount rising each time: \( 125+1=126 \), \( 126-2=124 \), \( 124+3=127 \), \( 127-4=123 \), and then \( 123+5=128 \). The last term is given as 129, so that is the wrong one.
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10, 26, 74, 218, 654, 1946, 5834
Answer: D
Correct answer: 654
Each term should be three times the one before, less four: \( 3(10)-4=26 \), \( 3(26)-4=74 \), \( 3(74)-4=218 \), and then \( 3(218)-4=650 \). The series gives 654 instead, so that is the wrong one; from 650 the rule resumes with 1946 and 5834.
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1, 2, 6, 15, 31, 56, 91
Answer: D
Correct answer: 91
The gaps should be the successive squares: \( 1, 4, 9, 16, 25, 36 \). They run correctly to 56, but the last step adds only 35, giving 91 where it should give \( 56 + 36 = 92 \). So 91 is the wrong term.
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3, 7, 15, 39, 63, 127, 255, 511
Answer: A
Correct answer: 39
Each term should be one less than a power of two: 3, 7, 15, 31, 63, 127, 255, 511. The fourth term is given as 39 where it should be 31, so that is the wrong one.
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56, 72, 90, 110, 132, 150
Answer: E
Correct answer: 150
Each term should be the product of two consecutive numbers: \( 7\cdot8=56 \), \( 8\cdot9=72 \), \( 9\cdot10=90 \), \( 10\cdot11=110 \), \( 11\cdot12=132 \), and then \( 12\cdot13=156 \). The series ends with 150 instead, so that is the wrong one.
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