Solve for a_n
a_{n}=\frac{S_{n}-n}{3}
Solve for S_n
S_{n}=n+3a_{n}
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3a_{n}+n=S_{n}
Swap sides so that all variable terms are on the left hand side.
3a_{n}=S_{n}-n
Subtract n from both sides.
\frac{3a_{n}}{3}=\frac{S_{n}-n}{3}
Divide both sides by 3.
a_{n}=\frac{S_{n}-n}{3}
Dividing by 3 undoes the multiplication by 3.
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Limits
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