Consider the set of numbers a, 2a, 3a, na where a and n are positive integers.

(a) show that the expression for the mean of this set is .

(b) let a = 4. find the minimum value of n for which the sum of these numbers

exceeds its mean by more than 100.

(a) The mean for this set is the total of the values divided by the number of values present in the set. That is,
                               average / mean = (a + 2a + 3a + ... + na) / n

(b) If a is 4, 2a = 8, na = 4n. Four the calculation,
              (4 + 8 + ... + 4n) - ((4 + 8 + ... + na) / n) = 100

     The value of n from the equation is approximately 7.8. The minimum value of n should be 8.