5. The integer $n$ is the mean of the three numbers 17,23 and $2 n$. What is the sum of the digits of $n$ ?
A 4
B 5
C 6
D 7
E 8
Solution
A
Because the mean of 17,23 and $2 n$ is $n$,
$$
\frac{17+23+2 n}{3}=n \text {, }
$$
and therefore,
$$
17+23+2 n=3 n,
$$
that is,
$$
40+2 n=3 n,
$$
from which it follows that
$$
n=40 \text {. }
$$

Therefore the sum of the digits of $n$ is $4+0=4$.
For INVESTIGATION
5.1 The integer $n$ is the mean of the four numbers $11,13,19$ and $3 n$. What is the value of $n$ ?
5.2 Let $k$ be a positive integer, with $k \geq 2$. Show that if $n$ is the mean of the $k$ numbers, $a_{1}, a_{2}, \ldots, a_{k-1}$ and $(k-1) n$, then $n=a_{1}+a_{2}+\cdots+a_{k-1}$.