Step 1: Recall the mechanism of \(S_N1\) reaction.
An \(S_N1\) reaction proceeds through a two-step mechanism.
The first and slowest step is the formation of a carbocation by the departure of the leaving group.
\[
R-X \rightarrow R^+ + X^-
\]
This step determines the rate of the reaction.
Step 2: Understand the role of the solvent.
The carbocation and the leaving group ion formed in the first step are charged species.
A solvent that can strongly solvate and stabilize these ions will facilitate carbocation formation and increase the rate of the \(S_N1\) reaction.
Step 3: Why polar protic solvents are preferred.
Polar protic solvents contain acidic hydrogen atoms and possess high dielectric constants.
Examples include
\[
H_2O,\ CH_3OH,\ C_2H_5OH
\]
These solvents stabilize both
\[
R^+
\]
and
\[
X^-
\]
through solvation.
As a result, carbocation formation becomes easier and the \(S_N1\) reaction proceeds readily.
Step 4: Analyze the other options.
Polar aprotic solvents generally favor \(S_N2\) reactions because they do not strongly solvate nucleophiles.
Non-polar solvents are poor at stabilizing ions and therefore do not favor carbocation formation.
Hence, they are not suitable for \(S_N1\) reactions.
Step 5: Final conclusion.
Therefore, \(S_N1\) reactions are generally carried out in
\[
\boxed{\text{Polar protic solvents}}
\]
Hence, the correct option is
\[
\boxed{(3)}
\]