9. An arithmetic series has first term \(a\) and common difference \(d\).
- Prove that the sum of the first \(n\) terms of the series is \(\frac { 1 } { 2 } n [ 2 a + ( n - 1 ) d ] .\)
(4)
A polygon has 16 sides. The lengths of the sides of the polygon, starting with the shortest side, form an arithmetic sequence with common difference \(d \mathrm {~cm}\).
The longest side of the polygon has length 6 cm and the perimeter of the polygon is 72 cm .
Find - the length of the shortest side of the polygon,
(5) - the value of \(d\).
(2) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\)
\end{tabular} & Leave blank
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{|l|l|}
\hline
\begin{tabular}{l}