, 2010

(a) Determine the average of the integers $71, 72, 73, 74, 75$. (b) Suppose that $n, n+1, n+2, n+3, n+4$ are five consecutive integers. (i) Determine a simplified expression for the sum of these five consecutive integers. (ii) If the average of these five consecutive integers is an odd integer, explain why $n$ must be an odd integer. (c) Six consecutive integers can be represented by $n, n+1, n+2, n+3, n+4, n+5$, where $n$ is an integer. Explain why the average of six consecutive integers is never an integer.