Solve for a_n
a_{n}=\frac{n+S_{n}}{2}
Solve for S_n
S_{n}=2a_{n}-n
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2a_{n}-n=S_{n}
Swap sides so that all variable terms are on the left hand side.
2a_{n}=S_{n}+n
Add n to both sides.
2a_{n}=n+S_{n}
The equation is in standard form.
\frac{2a_{n}}{2}=\frac{n+S_{n}}{2}
Divide both sides by 2.
a_{n}=\frac{n+S_{n}}{2}
Dividing by 2 undoes the multiplication by 2.
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