For an AP with first term u and common difference v, the `p^(th)` term is 15 uv more than the `q^(th)` term. Which one of the following is correct ?

Options

A. `p=q+15 v`
B. `p=q+15 u`
C. `p=q+14 v`
D. `p=q+14 u`

Answer

B

Explanation

Since first term and common difference of an AP are u and v respectively.
`p^(th)" term,"Tp=u+(p-1)v" "…(i)`
and `q^(th)" term," T_(q)=u+(q-1)v" "…(ii)`
According to condition given in question,
`implies" "T_(p)=T_(q)+15uv`
`implies" "T_(p)-T_(q)=15uv`
`implies" "u+(p-1)v-u-(q-1)v=15 uv`
`implies" "v(p-1-q+1)=15 uv`
`implies" "v(p-q)=15 uv`
`implies" "p-q=15uimpliesp=q+15u`