If the sum of m consecutive odd integers is `m^(4)` , then the first integer is

Options

A. `m^(3)+m+1`
B. `m^(3)+m-1`
C. `m^(3)-m-1`
D. `m^(3)-m+1`

Answer

D

Explanation

Let `2a+1,2a+3,2a+5,"...."` be the AP, then
`m^(4)=(2a+1)+(2a+3)+(2a+5)+"...."" upto n terms "`
`(m)/(2)={2(2a+1)+(m-1)*2}=m(2a+1+m-1)`
`implies (m)^(3)=(2a+1)+m-1`
`:.2a+1=m^(3)-m+1`