Determing a rule for each sequence using words and state if it is constant apferonce or ratio 2) \( 36 ; 32 ; 28 ; 24 ; 20 \) 3) \( 16 ; 4 ; 1 ; 0,25 ; 0.0625 \) 4) \( 6 ;-2 ;-\frac{2}{3} ;-\frac{2}{7} ;-\frac{2}{27} \) 5) \( 36 ; 49 ; 64 ; 81 ; 100 \)

Let's analyze each sequence step by step to determine the rule governing them and identify whether they are constant, arithmetic (constant difference), or geometric (constant ratio). ### Sequence 1: \( 36, 32, 28, 24, 20 \) 1. **Identify the differences:** - \( 32 - 36 = -4 \) - \( 28 - 32 = -4 \) - \( 24 - 28 = -4 \) - \( 20 - 24 = -4 \) 2. **Rule:** The sequence decreases by 4 each time. 3. **Type:** This is an arithmetic sequence with a constant difference of -4. ### Sequence 2: \( 16, 4, 1, 0.25, 0.0625 \) 1. **Identify the ratios:** - \( \frac{4}{16} = \frac{1}{4} \) - \( \frac{1}{4} = \frac{1}{4} \) - \( \frac{0.25}{1} = \frac{1}{4} \) - \( \frac{0.0625}{0.25} = \frac{1}{4} \) 2. **Rule:** Each term is multiplied by \( \frac{1}{4} \) to get the next term. 3. **Type:** This is a geometric sequence with a constant ratio of \( \frac{1}{4} \). ### Sequence 3: \( 6, -2, -\frac{2}{3}, -\frac{2}{7}, -\frac{2}{27} \) 1. **Identify the pattern:** - The first term is 6. - The second term is -2. - The third term is \( -\frac{2}{3} \). - The fourth term is \( -\frac{2}{7} \). - The fifth term is \( -\frac{2}{27} \). 2. **Identify the differences:** - The difference between the first and second term is \( -2 - 6 = -8 \). - The difference between the second and third term is \( -\frac{2}{3} - (-2) = -\frac{2}{3} + 2 = \frac{4}{3} \). - The differences do not form a constant pattern. 3. **Identify the ratios:** - \( \frac{-2}{6} = -\frac{1}{3} \) - \( \frac{-\frac{2}{3}}{-2} = \frac{1}{3} \) - \( \frac{-\frac{2}{7}}{-\frac{2}{3}} = \frac{3}{7} \) - \( \frac{-\frac{2}{27}}{-\frac{2}{7}} = \frac{7}{27} \) 4. **Rule:** The sequence does not follow a constant difference or ratio. It appears to be a more complex sequence. 5. **Type:** This sequence does not fit neatly into constant difference or ratio categories. ### Sequence 4: \( 36, 49, 64, 81, 100 \) 1. **Identify the differences:** - \( 49 - 36 = 13 \) - \( 64 - 49 = 15 \) - \( 81 - 64 = 17 \) - \( 100 - 81 = 19 \) 2. **Identify the pattern in differences:** - The differences are increasing by 2 each time. 3. **Rule:** The sequence consists of perfect squares: \( 6^2, 7^2, 8^2, 9^2, 10^2 \). 4. **Type:** This is neither an arithmetic nor a geometric sequence; it is a sequence of perfect squares. ### Summary of Findings: 1. **Sequence 1:** Arithmetic sequence with a constant difference of -4. 2. **Sequence 2:** Geometric sequence with a constant ratio of \( \frac{1}{4} \). 3. **Sequence 3:** Does not fit constant difference or ratio; more complex. 4. **Sequence 4:** Sequence of perfect squares; neither arithmetic nor geometric.