Determine the tenth and nth terms using a table and number sentence.

The terms are $13, 23, 33, 43$.
The difference between consecutive terms is $23 - 13 = 10$, $33 - 23 = 10$, $43 - 33 = 10$.
The common difference is 10.

Since the common difference is 10, the $n^{th}$ term will be of the form $10n + c$.
For $n=1$, the term is 13. So, $10(1) + c = 13 \implies 10 + c = 13 \implies c = 3$.
Thus, the $n^{th}$ term is $10n + 3$.

Substitute $n=10$ into the $n^{th}$ term formula:
$T_{10} = 10(10) + 3 = 100 + 3 = 103$.

The $n^{th}$ term is: $\boxed{\text{10n + 3}}$
The $10^{th}$ term is: $\boxed{\text{103}}$

The terms are $11, 17, 23, 29$.
The difference between consecutive terms is $17 - 11 = 6$, $23 - 17 = 6$, $29 - 23 = 6$.
The common difference is 6.

Since the common difference is 6, the $n^{th}$ term will be of the form $6n + c$.
For $n=1$, the term is 11. So, $6(1) + c = 11 \implies 6 + c = 11 \implies c = 5$.
Thus, the $n^{th}$ term is $6n + 5$.

Substitute $n=10$ into the $n^{th}$ term formula:
$T_{10} = 6(10) + 5 = 60 + 5 = 65$.

The $n^{th}$ term is: $\boxed{\text{6n + 5}}$
The $10^{th}$ term is: $\boxed{\text{65}}$

The terms are $17, 20, 23, 26$.
The difference between consecutive terms is $20 - 17 = 3$, $23 - 20 = 3$, $26 - 23 = 3$.
The common difference is 3.

Since the common difference is 3, the $n^{th}$ term will be of the form $3n + c$.
For $n=1$, the term is 17. So, $3(1) + c = 17 \implies 3 + c = 17 \implies c = 14$.
Thus, the $n^{th}$ term is $3n + 14$.

Substitute $n=10$ into the $n^{th}$ term formula:
$T_{10} = 3(10) + 14 = 30 + 14 = 44$.

The $n^{th}$ term is: $\boxed{\text{3n + 14}}$
The $10^{th}$ term is: $\boxed{\text{44}}$

The terms are $-16, -23, -30, -37$.
The difference between consecutive terms is $-23 - (-16) = -7$, $-30 - (-23) = -7$, $-37 - (-30) = -7$.
The common difference is $-7$.

Since the common difference is $-7$, the $n^{th}$ term will be of the form $-7n + c$.
For $n=1$, the term is $-16$. So, $-7(1) + c = -16 \implies -7 + c = -16 \implies c = -9$.
Thus, the $n^{th}$ term is $-7n - 9$.

Substitute $n=10$ into the $n^{th}$ term formula:
$T_{10} = -7(10) - 9 = -70 - 9 = -79$.

The $n^{th}$ term is: $\boxed{\text{-7n - 9}}$
The $10^{th}$ term is: $\boxed{\text{-79}}$