1. **Problem Statement:** Mr. Haley made a pattern with toothpicks: 9 in the 1st figure, 14 in the 2nd, 19 in the 3rd, and 24 in the 4th. We need to find: a) An algebraic expression for the nth term. b) The figure number with 94 toothpicks using a scatter plot. c) The number of toothpicks in the 10th figure using the scatter plot. d) Verify the results from (b) or (c) by substitution or guess and check. 2. **Finding the algebraic expression:** The pattern increases by 5 toothpicks each time (14-9=5, 19-14=5, 24-19=5), so this is an arithmetic sequence. The formula for the nth term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. Here, $a_1 = 9$ and $d = 5$, so: $$a_n = 9 + (n-1)5 = 9 + 5n - 5 = 5n + 4$$ 3. **Using the scatter plot to find the figure number for 94 toothpicks:** We set $a_n = 94$ and solve for $n$: $$94 = 5n + 4$$ $$94 - 4 = 5n$$ $$90 = 5n$$ $$n = \frac{90}{5} = 18$$ So, the 18th figure has 94 toothpicks. 4. **Using the scatter plot to find toothpicks in the 10th figure:** Substitute $n=10$ into the formula: $$a_{10} = 5(10) + 4 = 50 + 4 = 54$$ So, the 10th figure has 54 toothpicks. 5. **Verification by substitution:** For $n=18$: $$a_{18} = 5(18) + 4 = 90 + 4 = 94$$ This matches the toothpick count for the 18th figure. For $n=10$: $$a_{10} = 5(10) + 4 = 54$$ This matches the toothpick count for the 10th figure. **Final answers:** - Algebraic expression: $a_n = 5n + 4$ - Figure number with 94 toothpicks: 18 - Toothpicks in 10th figure: 54