Given :
$$ Q_n=\frac{R_1+R_2+...+R_{n-1}}{n-1} $$
$$ R = {1,2} $$
Is my calculation of $Q_n$ values correct ? :
$$ Q_1=\frac{1 + R_0}{0}=\frac{1 + 0}{1-0} ? $$
$$ Q_2=\frac{R_1+R_2+R_{2-1}}{2-1} =\frac{1+2+1}{2-1} ? $$
$$ R = {1,2,3,4,5} $$ therefore :
$$ Q_4=\frac{1+2+3}{3-1} ? $$
Not quite. Note that in this notation, $Q_1$ is not defined and then $$ \begin{split} Q_2 &= \frac{R_1}{2-1} = R_1\\ Q_3 &= \frac{R_1 + R_2}{3-1} = \frac{R_1 + R_2}{2}\\ Q_4 &= \frac{R_1 + R_2 + R_3}{4-1} = \frac{R_1 + R_2 + R_3}{3}\\ \ldots \end{split} $$
The intent, although somewhat obscure, was to define $$ Q_n = \frac{1}{n-1} \sum_{k=1}^{n-1} R_k, $$ in other words, the series $(Q_n)$ is really an average of $(R_n)$.
If you want to have a similar series with $Q_1$ defined, you can consider an alternative definition $$ Q_n = \frac{1}{n} \sum_{k=1}^n R_k. $$