In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern.
1, 9, 25, 49, 81, ?
Answer: C
Correct answer: 121
The terms are the squares of the odd numbers: \( 1^2, 3^2, 5^2, 7^2, 9^2 \), so the next is \( 11^2 = \mathbf{121} \).
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1, 9, 25, 49, ?, 121
Answer: B
Correct answer: 81
The terms are the squares of the odd numbers: \( 1^2, 3^2, 5^2, 7^2, \_ , 11^2 \). The missing one is \( 9^2 = \mathbf{81} \).
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1, 1, 4, 8, 9, 27, 16, ?
Answer: B
Correct answer: 64
Two series alternate. The odd places hold the squares - \( 1, 4, 9, 16 \) - and the even places the cubes - \( 1^3, 2^3, 3^3 \). The next cube is \( 4^3 = \mathbf{64} \).
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1, 2, 3, 6, 9, 18, ?, 54
Answer: B
Correct answer: 27
The series alternately doubles and adds the term before that: \( 1\times2=2 \), \( 2+1=3 \), \( 3\times2=6 \), \( 6+3=9 \), \( 9\times2=18 \), so next \[ 18 + 9 = \mathbf{27} \] and \( 27 \times 2 = 54 \), as shown.
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6, 13, 25, 51, 101, ?
Answer: C
Correct answer: 203
Each term is twice the one before, with one added and subtracted by turns: \( 2(6)+1=13 \), \( 2(13)-1=25 \), \( 2(25)+1=51 \), \( 2(51)-1=101 \), so \[ 2(101)+1 = \mathbf{203} \]
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5,6,9, 15, ?, 40
Answer: B
Correct answer: 25
The gaps are the triangular numbers: \( 6-5=1 \), \( 9-6=3 \), \( 15-9=6 \), so the next gap is 10, giving \[ 15 + 10 = \mathbf{25} \] and \( 25 + 15 = 40 \), as shown.
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1, 3, 4, 8, 15, 27, ?
Answer: C
Correct answer: 50
Each term from the fourth is the sum of the three before it: \( 1+3+4=8 \), \( 3+4+8=15 \), \( 4+8+15=27 \), so \[ 8+15+27 = \mathbf{50} \]
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198, 194, 185, 169, ?
Answer: D
Correct answer: 144
The amounts taken away are successive squares: \( 198-194=4 \), \( 194-185=9 \), \( 185-169=16 \). The next is \( 25 \), giving \[ 169 - 25 = \mathbf{144} \]
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2, 3, 5,7,11,?, 17
Answer: B
Correct answer: 13
The terms are the prime numbers in order - 2, 3, 5, 7, 11 - and the one that follows 11 is 13, with 17 coming after it as the series shows.
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6, 12, 21, ?, 48
Answer: A
Correct answer: 33
The gaps rise by three each time: \( 12-6=6 \), \( 21-12=9 \), then 12 and 15. So the missing term is \[ 21 + 12 = \mathbf{33} \] and \( 33 + 15 = 48 \), as shown.
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