Let's go through both questions in the image.

Question 5:

Given sequence: 5, 6, 7, 8...
You are asked to provide the recursive formula.

Solution:

This is an arithmetic sequence where each term increases by 1.

• Let $a_1 = 5$ (the first term).
• The rule for the next term $a_n$ is to add 1 to the previous term $a_{n-1}$.

Recursive formula:
$a_n = a_{n-1} + 1 \quad \text{with} \quad a_1 = 5$

Question 6:

Based on the visual pattern:
The image shows that each step increases the number of dots by adding 2 more dots than the previous step.

Analysis:

• Step 1: 1 dot
• Step 2: 3 dots (increased by 2)
• Step 3: 5 dots (increased by 2)
• Step 4: 7 dots (increased by 2)

This pattern increases by a fixed amount (2 dots each step), indicating an arithmetic sequence.

Answers:

1. Question 5 Recursive Formula:
   $a_n = a_{n-1} + 1 \quad \text{with} \quad a_1 = 5$

2. Question 6 Answer:
   ⭕ Arithmetic

Would you like further explanation or additional examples?

Related Questions:

1. What is the general formula for an arithmetic sequence?
2. How do you identify a geometric sequence?
3. What is the difference between recursive and explicit formulas?
4. How can you find the $n$-th term of an arithmetic sequence?
5. Can you graph an arithmetic sequence?

Tip:

In an arithmetic sequence, the difference between consecutive terms is always constant.