What is the arithmetic mean of `(1)/(2), (1)/(3), 2n` and m ?

Options

A. `(5+12n+6m)/(24)`
B. `(5+8n+4m)/(24)`
C. `(5+2n+m)/(4)`
D. `(5+12n+6m)/(6)`

Answer

A

Explanation

You can find the mean by adding these terms and dividing the sum by four, the number of terms in the set.
`(1)/(2)+(1)/(3)=(3)/(6)+(2)/(6)=(5)/(6)`
`(5)/(6)+2n = (5)/(6)+(12n)/(6)=(5+12n)/(6)`
`(5+12n)/(6)+m = (5+12n)/(6)+(6m)/(6)=(5+12n+6m)/(6)`
Now divide this sum by 4 :
`((5+12n+6m)/(6))/(4)=(5+12n+6m)/(6)xx(1)/(4)=(5+12n+6m)/(24)`