Question
Create your own sequence with a constant ratio
Answers
GPT-4o mini
Sure! A sequence with a constant ratio is called a geometric sequence. Here's an example:
Let's start with the first term, \( a_1 = 3 \), and choose a constant ratio (common ratio) \( r = 2 \).
The sequence will be:
1. \( a_1 = 3 \)
2. \( a_2 = a_1 \cdot r = 3 \cdot 2 = 6 \)
3. \( a_3 = a_2 \cdot r = 6 \cdot 2 = 12 \)
4. \( a_4 = a_3 \cdot r = 12 \cdot 2 = 24 \)
5. \( a_5 = a_4 \cdot r = 24 \cdot 2 = 48 \)
So, the geometric sequence is:
**3, 6, 12, 24, 48**
Each term is obtained by multiplying the previous term by 2!
Let's start with the first term, \( a_1 = 3 \), and choose a constant ratio (common ratio) \( r = 2 \).
The sequence will be:
1. \( a_1 = 3 \)
2. \( a_2 = a_1 \cdot r = 3 \cdot 2 = 6 \)
3. \( a_3 = a_2 \cdot r = 6 \cdot 2 = 12 \)
4. \( a_4 = a_3 \cdot r = 12 \cdot 2 = 24 \)
5. \( a_5 = a_4 \cdot r = 24 \cdot 2 = 48 \)
So, the geometric sequence is:
**3, 6, 12, 24, 48**
Each term is obtained by multiplying the previous term by 2!