Sullivan Chavez
03/14/2023 · Primary School
ge 61 Identify whether arithmetic, geometric, harmonic or \( 1,3,9,27, \ldots= \) geometric Fibonacci \( 1,3,5,7 \ldots= \)
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Let's analyze the sequences you've provided:
1. **Sequence: \( 1, 3, 9, 27, \ldots \)**
This sequence can be expressed as \( 3^0, 3^1, 3^2, 3^3, \ldots \). Each term is obtained by multiplying the previous term by 3. Therefore, this sequence is a **geometric sequence** with a common ratio of 3.
2. **Sequence: \( 1, 3, 5, 7, \ldots \)**
This sequence consists of odd numbers, and each term increases by 2 from the previous term. The difference between consecutive terms is constant (3 - 1 = 2, 5 - 3 = 2, etc.). Therefore, this sequence is an **arithmetic sequence** with a common difference of 2.
In summary:
- \( 1, 3, 9, 27, \ldots \) is a **geometric sequence**.
- \( 1, 3, 5, 7, \ldots \) is an **arithmetic sequence**.
Quick Answer
- \( 1, 3, 9, 27, \ldots \) is a geometric sequence.
- \( 1, 3, 5, 7, \ldots \) is an arithmetic sequence.
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