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If the sum of m consecutive odd integers...

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

A

`m^(3)+m+1`

B

`m^(3)+m-1`

C

`m^(3)-m-1`

D

`m^(3)-m+1`

Text Solution

Verified by Experts

The correct Answer is:
D
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`
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