70) Which of the following best describes the series 100 A) arithmetic; \( a=3, d=5 \) B) arithmetic; \( a=5, d=3 \) C) geometric; \( a=3, r=5 \) D) geometric; \( a=5, r=3 \)

It appears that the problem statement provided is incomplete or may have formatting issues. To accurately determine which option best describes the series, additional information about the series' terms or its pattern is necessary. Typically, to identify whether a series is arithmetic or geometric, and to determine its parameters (such as the first term \( a \), common difference \( d \), or common ratio \( r \)), you'll need to know multiple terms of the series or a specific rule that defines the series. **Here's what could help clarify the problem:** 1. **List of Terms:** Providing the first few terms of the series would allow us to identify whether it's arithmetic (constant difference between terms) or geometric (constant ratio between terms). 2. **General Formula:** If the series has a general term formula (e.g., \( a_n = a + (n-1)d \) for arithmetic or \( a_n = a \cdot r^{(n-1)} \) for geometric), that information would be crucial. 3. **Specific Pattern or Rule:** Any additional rules or patterns that the series follows would assist in determining its nature. **Example Clarification:** - **Arithmetic Series Example:** Suppose the series is \( 3, 8, 13, 18, \ldots \). This is an arithmetic series with the first term \( a = 3 \) and a common difference \( d = 5 \), which matches option **A**. - **Geometric Series Example:** If the series were \( 5, 15, 45, 135, \ldots \), it would be a geometric series with the first term \( a = 5 \) and a common ratio \( r = 3 \), corresponding to option **D**. If you can provide more details or clarify the series in question, I'd be happy to assist further in determining the correct option!