I see that you're working on finding the first four terms and the 10th term of the given sequences. Let's solve them one by one:

a) Sequence: $n + 5$

This is a linear sequence where each term increases by 1. For $n = 1, 2, 3, 4, \dots$, we can calculate the first four terms and the 10th term as follows:

• When $n = 1$, the term is $1 + 5 = 6$
• When $n = 2$, the term is $2 + 5 = 7$
• When $n = 3$, the term is $3 + 5 = 8$
• When $n = 4$, the term is $4 + 5 = 9$
• When $n = 10$, the term is $10 + 5 = 15$

So, the first four terms are: $6, 7, 8, 9$ And the 10th term is: $15$

b) Sequence: $2n - 1$

This is another linear sequence. For $n = 1, 2, 3, 4, \dots$, we can calculate the first four terms and the 10th term as follows:

• When $n = 1$, the term is $2(1) - 1 = 1$
• When $n = 2$, the term is $2(2) - 1 = 3$
• When $n = 3$, the term is $2(3) - 1 = 5$
• When $n = 4$, the term is $2(4) - 1 = 7$
• When $n = 10$, the term is $2(10) - 1 = 19$

So, the first four terms are: $1, 3, 5, 7$ And the 10th term is: $19$

Final Answers:

• For sequence $n + 5$: The first four terms are $6, 7, 8, 9$, and the 10th term is $15$.
• For sequence $2n - 1$: The first four terms are $1, 3, 5, 7$, and the 10th term is $19$.

Would you like further clarification or additional examples?

Here are some related questions to expand your understanding:

1. How would you write a general formula for any arithmetic sequence?
2. How does the formula for $n + 5$ compare with the formula for $2n - 1$?
3. What is the difference between an arithmetic sequence and a geometric sequence?
4. How can you find the nth term of any arithmetic sequence?
5. How do you determine the common difference in an arithmetic sequence?

Tip: Always check if the sequence is arithmetic (where each term increases or decreases by a constant amount) or if another type of pattern is involved!