The image you uploaded contains several sequences. Let me help break them down one by one:

f.
$\sqrt{5}, \ 1 + \sqrt{5}, \ 2 + \sqrt{5}, \ 3 + \sqrt{5}, \ldots$
This sequence appears to be an arithmetic progression where the common difference is 1, and each term is added to $\sqrt{5}$. The general form of the $n$-th term can be written as: $T_n = n + \sqrt{5}$

g.
$\frac{1}{2}, \ \frac{1}{3}, \ \frac{1}{4}, \ \frac{1}{5}, \ldots$
This sequence is a harmonic progression where the denominator increases by 1. The general term is: $T_n = \frac{1}{n+1}$ since the first term is $\frac{1}{2}$.

h.
$\frac{3}{16}, \ \frac{3}{8}, \ \frac{3}{4}, \ \frac{3}{2}, \ldots$
This is a geometric sequence where the first term is $\frac{3}{16}$, and the common ratio is 2. The general term of the sequence can be written as: $T_n = \frac{3}{16} \cdot 2^{n-1}$

i.
$a, \ ab, \ ab^2, \ ab^3, \ldots$
This is a geometric sequence where the first term is $a$, and the common ratio is $b$. The general term of the sequence is: $T_n = a \cdot b^{n-1}$

j.
$a, \ a + k^2, \ a + 2k^2, \ a + 3k^2, \ldots$
This appears to be an arithmetic sequence where the common difference is $k^2$. The general term can be written as: $T_n = a + (n-1)k^2$

Would you like more details on any of these sequences or have specific questions?

Here are some related questions for further exploration:

1. What is the sum of the first $n$ terms of a harmonic sequence (as in g)?
2. Can the sequence in h be written in summation form?
3. How does the general form of an arithmetic progression help solve real-world problems?
4. In sequence i, what happens if $b$ is a fraction or negative number?
5. How would you represent the sequence in j graphically?

Tip: In a geometric sequence, multiplying terms by a constant common ratio makes it easier to express the entire sequence using exponents.