1. **State the problem:** We are given a sequence with terms and their corresponding values: (1, 24), (2, 36), (3, 54), (4, 81). We need to find the rule that determines the consecutive y-coordinates (values) and then find the seventh term of another sequence: 4.8, 2.4, 1.2, 0.6, ... 2. **Analyze the first sequence:** The values are 24, 36, 54, 81. Let's check the differences and ratios: - Differences: 36 - 24 = 12, 54 - 36 = 18, 81 - 54 = 27 (not constant) - Ratios: $ \frac{36}{24} = 1.5 $, $ \frac{54}{36} = 1.5 $, $ \frac{81}{54} = 1.5 $ Since the ratio is constant at 1.5, the sequence is geometric with common ratio 1.5. 3. **Rule for consecutive y-coordinates:** Multiply by 1.5 (Option D). 4. **Analyze the second sequence:** 4.8, 2.4, 1.2, 0.6, ... - Check ratio: $ \frac{2.4}{4.8} = 0.5 $, $ \frac{1.2}{2.4} = 0.5 $, $ \frac{0.6}{1.2} = 0.5 $ This is a geometric sequence with common ratio 0.5. 5. **Find the seventh term:** The first term $ a_1 = 4.8 $, ratio $ r = 0.5 $. The formula for the nth term of a geometric sequence is: $$ a_n = a_1 \times r^{n-1} $$ Calculate the seventh term: $$ a_7 = 4.8 \times 0.5^{7-1} = 4.8 \times 0.5^6 $$ Calculate $ 0.5^6 = 0.015625 $, so: $$ a_7 = 4.8 \times 0.015625 = 0.075 $$ **Final answer:** The rule for the first sequence is to multiply by 1.5. The seventh term of the second sequence is 0.075.