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, ?, 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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2,2,5, 13,28,?
Answer: D
Correct answer: 52
The gaps are one less than successive squares: \( 2-2=0 \), \( 5-2=3 \), \( 13-5=8 \), \( 28-13=15 \) - that is \( 1^2-1, 2^2-1, 3^2-1, 4^2-1 \). The next gap is \( 5^2-1=24 \), giving \[ 28 + 24 = \mathbf{52} \]
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0, 2, 8, 14, ?, 34
Answer: C
Correct answer: 24
The gaps come in pairs: \( +2 \), then \( +6, +6 \), then \( +10, +10 \). From 14 the next step adds 10, giving \[ 14 + 10 = \mathbf{24} \] and \( 24 + 10 = 34 \), as shown.
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1, 5, 14, 30, 55, 91, ?
Answer: B
Correct answer: 140
Each term adds the next square: \( 1+4=5 \), \( 5+9=14 \), \( 14+16=30 \), \( 30+25=55 \), \( 55+36=91 \). The next square is 49, so \[ 91 + 49 = \mathbf{140} \]
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In the series 10, 17, 24, 31, 38,.....which of the following will be a number of the series ?
Answer: B
Correct answer: 346
The series rises by 7 each time from 10, so every term leaves a remainder of 3 when divided by 7. Of the numbers offered, only 346 does: \( 346 = 7 \times 49 + 3 \). The others leave remainders of 6, 0 and 2.
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240, ?, 120, 40, 10, 2.
Answer: B
Correct answer: 240
Each term is the one before divided by 1, 2, 3, 4, 5 in turn: \[ 240 \div 1 = 240,\; 240 \div 2 = 120,\; 120 \div 3 = 40,\; 40 \div 4 = 10,\; 10 \div 5 = 2 \] so the missing second term is 240.
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2,3,8,27, 112,?
Answer: D
Correct answer: 565
Each term is the one before multiplied by \( n \) and increased by \( n \), with \( n \) rising each step: \( 2(1)+1=3 \), \( 3(2)+2=8 \), \( 8(3)+3=27 \), \( 27(4)+4=112 \), so \[ 112 \times 5 + 5 = \mathbf{565} \]
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6, 17, 39, 72, ?
Answer: C
Correct answer: 116
The gaps are multiples of eleven: \( 17-6=11 \), \( 39-17=22 \), \( 72-39=33 \). The next gap is 44, giving \[ 72 + 44 = \mathbf{116} \]
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20, 20, 19, 16, 17, 13, 14, 11, ?, ?
Answer: A
Let the missing terms of the series be x1 and x2.
Thus, the sequence 20, 20, 19, 16, 17, 13, 14, 11, xv x2 is a combination of two series :
I. 20, 19, 17, 14, x1 and II. 20, 16, 13, 11, x2
The pattern in I is - 1, - 2, - 3,......So, missing term, x1 = 14 - 4 = 10.
The pattern in II is - 4, - 3, - 2,......So, missing term, x2 = 11 - 1 = 10.
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24, 60, 120, 210, ?
Answer: B
Correct answer: 336
Each term is the product of three consecutive numbers: \[ 2\cdot3\cdot4=24,\; 3\cdot4\cdot5=60,\; 4\cdot5\cdot6=120,\; 5\cdot6\cdot7=210 \] so the next is \( 6\cdot7\cdot8 = \mathbf{336} \).
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