Select the number from among the given options that can replace the question mark (?) in the following series.
4,8,16,64,36,216,64,?
- A512
- B432
- C343
- D729
Solution & Step-by-step Explanation
This series is an alternating combination of two separate sequences:
Series 1 (at odd positions): 4,16,36,64,…
These are squares of consecutive even numbers:
2
2
=4
4
2
=16
6
2
=36
8
2
=64
Series 2 (at even positions): 8,64,216,?
These are cubes of consecutive even numbers:
2
3
=8
4
3
=64
6
3
=216
Following this pattern, the next term in Series 2 must be the cube of 8:
8
3
=512
Series 1 (at odd positions): 4,16,36,64,…
These are squares of consecutive even numbers:
2
2
=4
4
2
=16
6
2
=36
8
2
=64
Series 2 (at even positions): 8,64,216,?
These are cubes of consecutive even numbers:
2
3
=8
4
3
=64
6
3
=216
Following this pattern, the next term in Series 2 must be the cube of 8:
8
3
=512