Question : Directions: In the following question, a series is given with one number missing. Select the missing number from the given alternatives.
14, 22, 37, 61, 96, ?
Option 1: 152
Option 2: 132
Option 3: 144
Option 4: 162
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Correct Answer: 144
Solution :
Given:
14, 22, 37, 61, 96, ?
Subtracting 1 from the squares of consecutive natural numbers (starting from 3) and then adding the resultant to the previous number, to get the next number in the series.
14 + {(3)
2
– 1} = 14 + {9 – 1} = 14 + 8 = 22
22 + {(4)
2
– 1} = 22 + {16 – 1} = 22 + 15 = 37
37 + {(5)
2
– 1} = 37 + {25 – 1} = 37 + 24 = 61
61 + {(6)
2
– 1} = 61 + {36 – 1} = 61 + 35 = 96
96 + {(7)
2
– 1} = 96 + {49 – 1} = 96 + 48 = 144
So, the required number is 144. Hence, the third option is correct.
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