Question
What kind of sequence is this? 117, 234, 468, 936, ...
Answers
Answered by
GPT-4o mini
The sequence you've provided is: 117, 234, 468, 936, ...
To identify the type of sequence, we can look at the pattern of how each term relates to the previous term. Let's examine the ratio between consecutive terms:
- \( \frac{234}{117} = 2 \)
- \( \frac{468}{234} = 2 \)
- \( \frac{936}{468} = 2 \)
Each term is multiplied by 2 to get to the next term in the sequence.
Since each term is obtained by multiplying the previous term by 2, this is a geometric sequence with a common ratio of 2. The general form of a term in this geometric sequence can be expressed as:
\[ a_n = 117 \times 2^{(n-1)} \]
where \( a_n \) is the \( n \)-th term in the sequence.
To identify the type of sequence, we can look at the pattern of how each term relates to the previous term. Let's examine the ratio between consecutive terms:
- \( \frac{234}{117} = 2 \)
- \( \frac{468}{234} = 2 \)
- \( \frac{936}{468} = 2 \)
Each term is multiplied by 2 to get to the next term in the sequence.
Since each term is obtained by multiplying the previous term by 2, this is a geometric sequence with a common ratio of 2. The general form of a term in this geometric sequence can be expressed as:
\[ a_n = 117 \times 2^{(n-1)} \]
where \( a_n \) is the \( n \)-th term in the sequence.