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Two consecutive number p,p + 1 are remov...

Two consecutive number p,p + 1 are removed from natural numbers. 1,2,3, 4……….., `n-1,` n such that arithmetic mean of these number reduces by 1, then (n-p) is equal to.

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
A
`A.M`. of `1,2,3,4,…….,n`
`((n(n+1))/(2))/(n) = (n+1)/(2)`
If `p,p+1` are removed then
`A.M.=((n(n+1))/(2)-(2p+1))/(n-2)`
` therefore 1=((n+1)/(2))-((n(n+1)-2(2p+1))/(2.(n-2)))`
`implies(n-p)=1`
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