Two consecutive numbers from 1,2,3 …., n are removed.The arithmetic mean of the remaining numbers is 105/4 .
The removed numbers

Options

A. a-b=d-c
B. e=0
C. `a,b-2//3,c-1 " are in " in A.P`
D. `(b+d)//a` is an integer

Answer

A, B, C, D

Explanation

`an^(4)+bn^(3)+cn^(3)+dn+e`
`=2sum_(r=1)^(n)r(r+1)(r+2)-sum_(r=1)^(n)r(r+1)`
`=2/4n(n+1)(n+2)(n+3)-1/3n(n+1)(n+2)`
`=1/6(3n^(4)+16n^(3)+27n^(2)+14n)`