Select the number from among the given options that can replace the question mark (?) in the following series.
4, 27, 16, 125, ?, 343
- A216
- B64
- C36
- D512
Solution & Step-by-step Explanation
Let's analyze the terms of the series:
1
st
term=4=2
2
2
nd
term=27=3
3
3
rd
term=16=4
2
4
th
term=125=5
3
5
th
term=?=6
2
6
th
term=343=7
3
The series alternates between the squares and cubes of consecutive natural numbers starting from 2.
Therefore, the missing term is 6
2
=36.
1
st
term=4=2
2
2
nd
term=27=3
3
3
rd
term=16=4
2
4
th
term=125=5
3
5
th
term=?=6
2
6
th
term=343=7
3
The series alternates between the squares and cubes of consecutive natural numbers starting from 2.
Therefore, the missing term is 6
2
=36.