Solution for Image 1 (3A):

The nth term of the sequence is given as $3n + 7$. To find the first three terms, substitute $n = 1$, $n = 2$, and $n = 3$ into the formula:

1. For $n = 1$: $3(1) + 7 = 3 + 7 = 10$

2. For $n = 2$: $3(2) + 7 = 6 + 7 = 13$

3. For $n = 3$: $3(3) + 7 = 9 + 7 = 16$

First three terms: 10, 13, 16

Solution for Image 2 (3D):

The sequence provided is 8, 15, 22, 29. To find the $n$-th term rule:

1. Find the common difference: $15 - 8 = 7$, $22 - 15 = 7$, $29 - 22 = 7$.

   The common difference $d = 7$.

2. Find the first term ($a$): $a = 8$.

3. General formula for an arithmetic sequence: $a_n = a + (n-1)d$

4. Substitute $a = 8$ and $d = 7$ into the formula: $a_n = 8 + (n-1) \cdot 7$ Simplify: $a_n = 8 + 7n - 7 = 7n + 1$

The nth term rule: $7n + 1$

Let me know if you need more detailed steps or have further questions!

Relative Questions:

1. How can we check if a sequence is arithmetic or geometric?
2. Can you derive the nth term formula for any arithmetic sequence?
3. What happens if the common difference is negative in an arithmetic sequence?
4. How do we find the sum of the first $n$ terms in an arithmetic sequence?
5. How can the nth term formula help in solving word problems related to sequences?

Tip:

Always test your nth term formula by substituting small values of $n$ to ensure it produces the correct sequence values.