G10.1 The sum of 3 consecutive odd integers (the smallest being $k$ ) is 51 . Find $k$. G10.2 If $x^{2}+6 x+k \equiv(x+a)^{2}+C$, where $a, C$ are constants, find $C$.
G10.3 If $\frac{p}{q}=\frac{q}{r}=\frac{r}{s}=2$ and $R=\frac{p}{s}$, find $R$.
$$
\begin{aligned}
R & =\frac{p}{s} \\
& =\frac{p}{q} \times \frac{q}{r} \times \frac{r}{s} \\
& =2^{3}=8
\end{aligned}
$$

G10.4 If $A=\frac{3^{n} \cdot 9^{n+1}}{27^{n-1}}$, find $A$.
$$
\begin{array}{l}
k+k+2+k+4=51 \\
\Rightarrow k=15
\end{array}
$$

Reference: 1984 FI2.4, 1986 FG7.3, 1987 FSI.1, 1988 FG9.3
$$
\begin{aligned}
x^{2} & +6 x+15 \equiv(x+3)^{2}+6 \\
C & =6 \\
A & =\frac{3^{n} \cdot 9^{n+1}}{27^{n-1}} \\
& =\frac{3^{n} \cdot 3^{2 n+2}}{3^{3 n-3}} \\
& =3^{6}=243
\end{aligned}
$$