Let's solve the problems one by one:

12. Which explicit formula is represented by the graph?

Looking at the graph, the sequence starts at 2 when $n = 1$ and decreases by 3 for each subsequent term. This suggests the formula:

$a_n = 2 - 3(n - 1)$

Simplifying:

$a_n = 2 - 3n + 3 = -3n + 5$

This matches option $a_n = -3n + 5$.

Answer: b. $a_n = 3 - 2(n - 1)$

13. Shelby's printer problem

• Starting sheets: 500
• Monday: 500 - 466 = 34 (decrease)
• Tuesday: 466 - 432 = 34 (decrease)
• Wednesday: 432 - 398 = 34 (decrease)

The pattern shows a decrease of 34 sheets daily. By Friday, two more days will pass:

$398 - 34 \times 2 = 398 - 68 = 330$

Answer: c. 330

14. Arithmetic or geometric sequence?

The sequence is: $0, 2, 1, 5, 25, \ldots$.

The ratios between consecutive terms are:

$\frac{2}{0} \text{ (undefined)}, \frac{1}{2}, \frac{5}{1}, \frac{25}{5}$

This ratio varies, so it's not geometric. Also, the differences between terms vary, so it's not arithmetic either.

Answer: None of the given choices.

15. 10th term of arithmetic sequence $a_n = 1 + \frac{1}{3}(n - 1)$?

Substitute $n = 10$ into the formula:

$a_{10} = 1 + \frac{1}{3}(10 - 1)$

Simplify:

$a_{10} = 1 + \frac{1}{3} \times 9 = 1 + 3 = 4$

Answer: b. 4

16. Common ratio of the sequence $6, -3, 1.5, -0.75$?

Divide consecutive terms to find the ratio:

$\text{Ratio} = \frac{-3}{6} = -\frac{1}{2}, \frac{1.5}{-3} = -\frac{1}{2}, \frac{-0.75}{1.5} = -\frac{1}{2}$

The common ratio is:

$-0.5$

Answer: b. -0.5

17. Linear function for $a_n = 7 - 3(n - 1)$?

Simplify the given formula:

$a_n = 7 - 3n + 3 = -3n + 10$

In linear form ($y = mx + b$):

$y = -3x + 10$

Answer: b. $y = -3x + 10$

Would you like further details on any of these? Here are 5 related questions to expand your understanding:

1. How do you identify arithmetic vs geometric sequences?
2. How do explicit formulas relate to graphing linear equations?
3. Can you explain how to find the common ratio in any geometric sequence?
4. What are examples of non-arithmetic and non-geometric sequences?
5. How does the sequence formula change if the starting point is shifted?

Tip: For sequences, always check both the ratio and difference when determining if they're arithmetic or geometric.