If the average (arithmetic mean) of three consecutive integers is k + 1, then the product of the greatest and least integer is
Choose the correct choice from the following choices.
A) k2 - 9  B) k^2 + 2k  C) k2 + 4k - 5  D) k2 + 6k + 9  E) k2 + 4k - 12
n = smallest number   n+2 = largest number   (n + n + 2)/2 = k+1   =&gt; (2n+2)/2 = k+ 1   =&gt; n + 1 = k + 1   =&gt; n = k   So Product of n and n+2 = (k)(k+2)   =k^2 + 2k   Answer - k^2 + 2k
<result>B</result>
If the average (arithmetic mean) of three consecutive integers is k + 1, then the product of the greatest and least integer is