The sequence 10000, 121, 100, 31, 24, ?, 20 represent a number x with respect to different bases. The missing number in this sequence is

Options

A. 16
B. 21
C. 10
D. 22

Answer

D

Explanation

The given sequence follows the pattern:
Number with base 2 :
`(10000)_(2)=ul(1xx2^(ul(4)))+ul(0xx2^(ul(3)))+ul(0xx2^(ul(2)))+ul(0xx2^(ul(1)))+ul(0xx2^(ul(0)))=2^(4)=16`.
Number with base 3 :
`(121)_(3)= ul(1xx3^(ul(2)))+ul(2xx3^(ul(1)))+ul(1xx3^(ul(0)))=9+6+1=1`
Number with base 4 :
`(100)_(4)=ul(1xx4^(ul(2)))+ul(0xx4^(ul(1)))+ul(0xx4^(ul(0)))=4^(2)=16.`
Number with base 5 :
`(ul(3)" "ul(1))_(5)=ul(3xx5^(ul(1)))+ul(1xx5^(ul(0)))=15+1=16.`
Number with base 6 :
`(ul(2)" "ul(4))_(6)=ul(2xx6^(ul(1)))+ul(4xx6^(ul(0)))=12+4=16.`
Number with base 7 :
`(ul(2)" "ul(2))_(7)=ul(2xx7^(ul(1)))+ul(4xx6^(ul(0)))=14+2=16.`
Number with base 8 :
`(ul(2)" "ul(0))_(8)=ul(2xx8^(ul(1)))+ul(0xx8^(ul(0)))=16+0=16`.
Therefore, Missing number = [22].