The given formula is
[tex]S= \frac{n}{2} (a_{1}+a_{n})[/tex]
Multiply each side by 2.
[tex]2S=n(a_{1}+a_{n}) [/tex]
Divide each side by n.
[tex] \frac{2S}{n} =a_{1} + a_{n}[/tex]
Subtract a₁ from each side.
[tex] \frac{2S}{n} - a_{1} = a_{n}[/tex]
Answer: [tex]a_{n} = \frac{2S}{n} - a_{1} [/tex]
