Answer:
[tex]a_n = 2S - a_1[/tex]
Step-by-step explanation:
Given
[tex]S = \frac{a_1 + a_n}{2}[/tex]
Required
Determine the formula for [tex]a_n[/tex]
What this question implies is to solve for [tex]a_n[/tex]
[tex]S = \frac{a_1 + a_n}{2}[/tex]
Multiply both sides by 2
[tex]2 * S = \frac{a_1 + a_n}{2} * 2[/tex]
[tex]2 S = a_1 + a_n[/tex]
Subtract [tex]a_1[/tex] from both sides
[tex]2S - a_1 = a_1 - a_1 + a_n[/tex]
[tex]2S - a_1 = a_n[/tex]
[tex]a_n = 2S - a_1[/tex]
Hence; the formula to solve [tex]a_n[/tex] is [tex]a_n = 2S - a_1[/tex]
