If the first, fifth and last terms of an `A.P.` is `l`, `m`, `p`, respectively, and sum of the `A.P.` is `((l+p)(4p+m-5l))/(k(m-l))` then `k` is

Options

A. `2`
B. `3`
C. `4`
D. `5`

Answer

A

Explanation

`(a)` Let common difference `=d` and number of terms `=n`
`:.T_(s)=m=l+4dimpliesd=(m-l)//4`
`:.T_(n)=p=l+((n-1)(m-1))/(4)`
`implies n=((4P+m-5)/(m-1))`
`:.` Sum of `n` terms of `A.P.=(n)/(2)["First term"+"Last term"]`
`=[(4p+m-5l)/(m-l)]*(1)/(2)[l+p]`........`(i)`
Comparing equation `(i)` with the given summation, we get `k=2`.