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

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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.
The arithmetic sequences are: - $$1, -1, -3, -5, -7, \ldots$$ - $$0.75, 1.5, 2.25, 3, 3.75, \ldots$$

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

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