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.
48, 24, 96, 48, 192, ?
Answer: C
Correct answer: 96
The series alternately halves and quadruples: \( 48 \div 2 = 24 \), \( 24 \times 4 = 96 \), \( 96 \div 2 = 48 \), \( 48 \times 4 = 192 \), so the next step halves: \[ 192 \div 2 = \mathbf{96} \]
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2,15,41,80,?
Answer: D
Correct answer: 132
The gaps are multiples of thirteen: \( 15-2=13 \), \( 41-15=26 \), \( 80-41=39 \). The next gap is \( 52 \), giving \[ 80 + 52 = \mathbf{132} \]
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Find the next term: 8, 24, 12, 36, 18, ?
Answer: C
Correct answer: 54
The series alternates between multiplying by 3 and dividing by 2.
\[8 \times 3 = 24, \quad 24 \div 2 = 12, \quad 12 \times 3 = 36, \quad 36 \div 2 = 18\]
The next step is a multiplication, giving \(18 \times 3 = 54\).
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Find the next term: 2, 5, 10, 17, 26, ?
Answer: D
Correct answer: 37
The differences between consecutive terms are 3, 5, 7, 9 - the odd numbers in order - so the next difference is 11.
\[26 + 11 = 37\]
Equivalently each term is \(n^2 + 1\), and the sixth term is \(6^2 + 1 = 37\).
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Find the next term: 120, 60, 20, 5, ?
Answer: C
Correct answer: 1
The divisor increases by one at each step.
\[120 \div 2 = 60, \quad 60 \div 3 = 20, \quad 20 \div 4 = 5\]
The next division is by 5, giving \(5 \div 5 = 1\).
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Find the next term: 11, 13, 17, 19, 23, ?
Answer: C
Correct answer: 29
The terms are consecutive prime numbers beginning at 11. After 23 the next prime is 29, since 25 is \(5 \times 5\), 26 and 28 are even, and 27 is \(3^3\).
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Find the next term: 1, 8, 27, 64, ?
Answer: C
Correct answer: 125
The terms are the cubes of the natural numbers.
\[1^3 = 1, \quad 2^3 = 8, \quad 3^3 = 27, \quad 4^3 = 64\]
The next is \(5^3 = 125\). Answering 100 mistakes the pattern for squares.
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Find the next term: 5, 11, 23, 47, ?
Answer: C
Correct answer: 95
Each term is double the one before it plus 1.
\[5 \times 2 + 1 = 11, \quad 11 \times 2 + 1 = 23, \quad 23 \times 2 + 1 = 47\]
So the next term is \(47 \times 2 + 1 = 95\).
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Find the next term: 7, 14, 28, 56, ?
Answer: B
Correct answer: 112
Each term is double the previous one, so the series is a geometric progression with common ratio 2.
\[56 \times 2 = 112\]
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Find the next term: 3, 8, 18, 38, ?
Answer: C
Correct answer: 78
Each term is twice the previous term plus 2.
\[3 \times 2 + 2 = 8, \quad 8 \times 2 + 2 = 18, \quad 18 \times 2 + 2 = 38\]
So the next term is \(38 \times 2 + 2 = 78\).
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