Let's solve the problem step by step.

Task:
For each sequence:

1. Determine the common difference (sequence generator).
2. Write the formula for the n-th term in the sequence.

Solution:

(a) 4, 7, 10, 13, ...

1. Common difference:
   $7 - 4 = 3$, $10 - 7 = 3$, $13 - 10 = 3$.
   The common difference $d = 3$.

2. Formula for the n-th term:
   The formula for the n-th term of an arithmetic sequence is:
   $t(n) = t(1) + (n-1)d$
   Substituting $t(1) = 4$ and $d = 3$:
   $t(n) = 4 + (n-1)(3) = 4 + 3n - 3 = 3n + 1$

(b) 3, 8, 13, ...

1. Common difference:
   $8 - 3 = 5$, $13 - 8 = 5$.
   The common difference $d = 5$.

2. Formula for the n-th term:
   Substituting $t(1) = 3$ and $d = 5$:
   $t(n) = 3 + (n-1)(5) = 3 + 5n - 5 = 5n - 2$

(c) 24, 19, 14, ...

1. Common difference:
   $19 - 24 = -5$, $14 - 19 = -5$.
   The common difference $d = -5$.

2. Formula for the n-th term:
   Substituting $t(1) = 24$ and $d = -5$:
   $t(n) = 24 + (n-1)(-5) = 24 - 5n + 5 = -5n + 29$

(d) 7, 9.5, 12, ...

1. Common difference:
   $9.5 - 7 = 2.5$, $12 - 9.5 = 2.5$.
   The common difference $d = 2.5$.

2. Formula for the n-th term:
   Substituting $t(1) = 7$ and $d = 2.5$:
   $t(n) = 7 + (n-1)(2.5) = 7 + 2.5n - 2.5 = 2.5n + 4.5$

Final Answers:

(a) $t(n) = 3n + 1$
(b) $t(n) = 5n - 2$
(c) $t(n) = -5n + 29$
(d) $t(n) = 2.5n + 4.5$

Would you like more details on any part of this solution?
Here are 5 related questions to explore further:

1. How do you derive the general formula for an arithmetic sequence?
2. What are other ways to find the common difference?
3. Can the common difference be a fraction or decimal?
4. How do you verify if a sequence is arithmetic?
5. What happens if the common difference is 0?

Tip: Always double-check the common difference before creating the formula!