Select every sequence that is arithmetic. \( \square 6,12,24,48,96 \ldots \) \( \square 1,-1,-3,-5,-7 \ldots \) \( \square 0.75,1.5,2.25,3,3.75 \ldots \) \( \square 4,6,9,13.5, \ldots \) \( \square 1,1,2,3,5,8,13 \ldots \)

To determine which of the given sequences are **arithmetic**, let's recall that an **arithmetic sequence** is one where the **difference between consecutive terms is constant**. This constant difference is known as the **common difference**. Let's analyze each sequence: 1. **\( \square \, 6, 12, 24, 48, 96, \ldots \)** - **Differences:** \(12 - 6 = 6\), \(24 - 12 = 12\), \(48 - 24 = 24\), \(96 - 48 = 48\) - **Observation:** The differences are \(6, 12, 24, 48, \ldots\), which are not constant. - **Conclusion:** **Not** an arithmetic sequence. 2. **\( \square \, 1, -1, -3, -5, -7, \ldots \)** - **Differences:** \(-1 - 1 = -2\), \(-3 - (-1) = -2\), \(-5 - (-3) = -2\), \(-7 - (-5) = -2\) - **Observation:** All differences are \(-2\). - **Conclusion:** **Arithmetic** with a common difference of \(-2\). 3. **\( \square \, 0.75, 1.5, 2.25, 3, 3.75, \ldots \)** - **Differences:** \(1.5 - 0.75 = 0.75\), \(2.25 - 1.5 = 0.75\), \(3 - 2.25 = 0.75\), \(3.75 - 3 = 0.75\) - **Observation:** All differences are \(0.75\). - **Conclusion:** **Arithmetic** with a common difference of \(0.75\). 4. **\( \square \, 4, 6, 9, 13.5, \ldots \)** - **Differences:** \(6 - 4 = 2\), \(9 - 6 = 3\), \(13.5 - 9 = 4.5\) - **Observation:** The differences are \(2, 3, 4.5, \ldots\), which are not constant. - **Conclusion:** **Not** an arithmetic sequence. 5. **\( \square \, 1, 1, 2, 3, 5, 8, 13, \ldots \)** - **Differences:** \(1 - 1 = 0\), \(2 - 1 = 1\), \(3 - 2 = 1\), \(5 - 3 = 2\), \(8 - 5 = 3\), \(13 - 8 = 5\) - **Observation:** The differences are \(0, 1, 1, 2, 3, 5, \ldots\), which are not constant. - **Conclusion:** **Not** an arithmetic sequence. ### **Summary** The **arithmetic sequences** among the given options are: - **\( \square \, 1, -1, -3, -5, -7, \ldots \)** - **\( \square \, 0.75, 1.5, 2.25, 3, 3.75, \ldots \)** These sequences have a **constant difference** between consecutive terms, fulfilling the criteria for an arithmetic sequence.