If the average (arithmetic mean) of seven consecutive integers is k - 2, then the product of the greatest and least integer is  Choose the correct choice from the following options
A) k2 - 9  B) k2 - 2k + 1  C) k2 - 4k - 5  D) k2 + 6k + 9  E) k2 + 4k - 12
n = smallest number   n+6 = largest number   (n + n + 6)/2 = k - 2   =&gt; (2n+6)/2 = k - 2   =&gt; n + 3 = k - 2   =&gt; n = k - 5   So Product of n and n+6 = (k-5)(k+1)   = k^2 - 5k + k - 5   = k^2 - 4k - 5   Answer - k2 - 4k - 5
<result>C</result>
If the average (arithmetic mean) of seven consecutive integers is k - 2, then the product of the greatest and least integer is