Question : Directions: Study the given pattern carefully and find the missing number.
(1, 1, 1, –1), (2, 4, 8, 2), (________, 36, 216, 174)
Option 1: 6
Option 2: 24
Option 3: 18
Option 4: 22
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Correct Answer: 6
Solution :
Given:
(1, 1, 1, –1), (2, 4, 8, 2), (________, 36, 216, 174)
In the above–given set of numbers, the second number is the square of the first number, and the third number is the cube of the first number. Add the first number and its square, then subtract the resultant from the cube of the first number to get the fourth number.
(1, 1, 1, –1)→1; (1)
2
= 1; (1)
3
= 1; (1)
3
– {(1)
2
+ 1} = 1 – {1 + 1} = 1 – 2 = –1
(2, 4, 8, 2)→2; (2)
2
= 4; (2)
3
= 8; (2)
3
– {(2)
2
+ 2} = 8 – {4 + 2} = 8 – 6 = 2
Similarly, (________, 36, 216, 174)→6; (6)
2
= 36; (6)
3
= 216; (6)
3
– {(6)
2
+ 6} = 216 – {36 + 6} = 216 – 42 = 174
So, 6 is the missing number. Hence, the first option is correct.
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