For the sequence, determine if the divergence test applies and either state that $\lim _{n \rightarrow \infty} a_{n}$ does not exist or find $\lim _{n \rightarrow \infty} a_{n}$. (If an answer does not exist, enter DNE.)
\[
\begin{array}{r}
a_{n}=\frac{2^{n}+3^{n}}{10^{n / 2}} \\
\lim _{n \rightarrow \infty} a_{n}=
\end{array}
\]

Step 1 ：The divergence test states that if the limit of a sequence as n approaches infinity is not zero, then the series diverges. In this case, we need to find the limit of the sequence as n approaches infinity.

Step 2 ：We can see that the numerator grows exponentially faster than the denominator, as the base of the exponent in the numerator is larger than the base of the exponent in the denominator. Therefore, we can expect that the limit as n approaches infinity will be infinity, which means the series diverges.

Step 3 ：However, to confirm this, we can calculate the limit numerically by evaluating the sequence for large values of n.

Step 4 ：The limit of the sequence as n approaches infinity is 0. This means that the divergence test does not apply, as the limit is not non-zero. Therefore, we cannot conclude that the series diverges based on the divergence test.

Step 5 ：Final Answer: The limit of the sequence as n approaches infinity is \(\boxed{0}\).