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.
Which term of the series 5, 10, 20, 40, ..... is 1280?
Answer: B
Clearly, 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40,.....
So, the series is a G.P. in which a = 5 and r = 2.
Let 1280 be the rath term of the series.
Then, 5x2n-1 = 1280 2n-1 = 256 = 28 n - 1 = 8 n = 9.
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2, 5, 9, ?, 20, 27
Answer: A
Correct answer: 14
The gaps between the terms increase by one each time: \[ 5-2=3,\quad 9-5=4,\quad \_-9=5,\quad 20-\_=6,\quad 27-20=7 \] so the missing term is \( 9 + 5 = \mathbf{14} \).
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2, 3, 3, 5, 10, 13, ?, 43, 172, 177
Answer: C
Correct answer: 39
The series alternately adds and multiplies, the number used rising by one each round: \( 2+1=3 \), \( 3\times1=3 \), \( 3+2=5 \), \( 5\times2=10 \), \( 10+3=13 \), so next \[ 13 \times 3 = \mathbf{39} \] and then \( 39+4=43 \), \( 43\times4=172 \), \( 172+5=177 \), as shown.
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9, 27, 31, 155, 161, 1127, ?
Answer: B
Correct answer: 1135
The operations alternate, the numbers used rising each time: \( \times 3 \), \( +4 \), \( \times 5 \), \( +6 \), \( \times 7 \), and then \( +8 \): \[ 1127 + 8 = \mathbf{1135} \]
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2, 1, 2, 4, 4, 5, 6, 7, 8, 8, 10, 11, ?
Answer: B
The given sequence is a combination of three series :
I. 1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8, ?
II. 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10
III. 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11
Clearly, I consists of consecutive even numbers. So, the missing term is 10.
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Which of the following will not be a number of the series 1, 8, 27, 64, 125,.....?
Answer: A
Correct answer: 256
The series is the perfect cubes: \( 1^3, 2^3, 3^3, 4^3, 5^3 \), continuing \( 6^3=216 \), \( 7^3=343 \), \( 8^3=512 \), \( 9^3=729 \), \( 10^3=1000 \). 256 is \( 2^8 \) and not a cube, so it cannot belong.
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13, 32, 24, 43, 35, ?, 46, 65, 57, 76
Answer: C
Correct answer: 54
Two series alternate, each rising by eleven. The first, at the odd places, runs 13, 24, 35, 46, 57; the second, at the even places, runs 32, 43, …, 65, 76. The missing term belongs to the second, so \[ 43 + 11 = \mathbf{54} \]
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22, 24, 28, ?, 52, 84
Answer: A
Correct answer: 36
The gaps double each time: \( 24-22=2 \), \( 28-24=4 \), then 8, 16 and 32. So the missing term is \[ 28 + 8 = \mathbf{36} \] and \( 36+16=52 \), \( 52+32=84 \), as shown.
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3, 15, ?, 63, 99, 143
Answer: B
Correct answer: 35
Each term is one less than the square of an even number: \[ 2^2-1=3,\; 4^2-1=15,\; 6^2-1=35,\; 8^2-1=63,\; 10^2-1=99,\; 12^2-1=143 \] so the missing term is 35.
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90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3
Answer: A
Correct answer: 150
Read in threes, the numbers 50, 100, 200 double each time, and the group that follows opens with 150 - the product of the two numbers that come after it, since \( 3 \times 50 = 150 \).
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