Answer:
[tex]\begin{equation*} a_n=\frac{2S-a_1n}{n} \end{equation*}[/tex]Explanation:
Given:
[tex]S=\frac{n(a_1+a_n)}{2}[/tex]To find:
[tex]a_n[/tex]We'll follow the below steps to solve for a_n;
Step 1: Find the cross product;
[tex]2S=n(a_1+a_n)[/tex]Step 2: Divide both sides by n;
[tex]\begin{gathered} \frac{2S}{n}=\frac{n(a_1+a_n)}{n} \\ \frac{2S}{n}=a_1+a_n \end{gathered}[/tex]Step 3: Subtract a_1 from both sides of the equation;
[tex]\begin{gathered} \frac{2S}{n}-a_1=a_1-a_1+a_n \\ \frac{2S}{n}-a_1=a_n \\ \frac{2S-a_1n}{n}=a_n \\ \therefore a_n=\frac{2S-a_{1}n}{n} \end{gathered}[/tex]