Question : Directions: In the following question, a series is given with one number missing. Select the missing number from the given alternatives.
3, 8, 5, 27, 8, 64, 12, 125, 17, ?
Option 1: 216
Option 2: 361
Option 3: 625
Option 4: 441
Correct Answer: 216
Solution :
Given:
3, 8, 5, 27, 8, 64, 12, 125, 17, ?
The series follows an alternative pattern, where every other number, starting from the first, is obtained by adding consecutive numbers in each previous term to get the next term. On the other hand, every other number, starting from the second, is obtained by cubing consecutive positive integers.
First alternate series –
3; 3 + 2 = 5; 5 + 3 = 8; 8 + 4 = 12; 12 + 5 = 17
Second alternate series –
(2)
3
= 8; (3)
3
= 27; (4
)
3
=
64; (5
)
3
=
125; (6
)
3
=
216
The missing number is 216. Hence, the first option is correct.
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