The average of 7 consecutive whole numbers is 7. Then 1 is added to the first number, 2 is added to the second number, 3 is added to the third number, and so on. What is the average of the seven new numbers?
Let the seven consecutive whole numbers be $n,$ $n+1,$ $n+2,$ $n+3,$ $n+4,$ $n+5,$ and $n+6.$ Their average is then
\[\frac{7n + 21}{7} = n + 3.\]Therefore, $n + 3 = 7,$ so $n = 4.$ Then the seven numbers are
\begin{align*}
5, 6, 7, 8, 9, 10, 11.
\end{align*}Adding 1 to the first number, 2 to the second number, 3 to the third number, etc., gives us:
\begin{align*}
5 + 1 &= 6, \\
6 + 2 &= 8, \\
7 + 3 &= 10, \\
8 + 4 &= 12, \\
9 + 5 &= 14, \\
10 + 6 &= 16, \\
11 + 7 &= 18.
\end{align*}Thus, the average of the new numbers is $\frac{6+8+10+12+14+16+18}{7} = \boxed{12}.$