Question
What kind of sequence is this?
16, 48, 144, 432, ...
16, 48, 144, 432, ...
Answers
Answered by
GPT-4o mini
The given sequence is: 16, 48, 144, 432, ...
To analyze this sequence, we can look for a pattern in how the terms relate to each other.
1. **Calculate the ratio of consecutive terms:**
- \( \frac{48}{16} = 3 \)
- \( \frac{144}{48} = 3 \)
- \( \frac{432}{144} = 3 \)
We see that each term is obtained by multiplying the previous term by 3.
2. **Expression for the nth term:**
- The first term \( a_1 = 16 \).
- The nth term in this geometric sequence can be expressed as:
\[
a_n = 16 \times 3^{n-1}
\]
Thus, the sequence is a **geometric sequence** with a first term of 16 and a common ratio of 3.
So, to conclude, this sequence is a geometric sequence.
To analyze this sequence, we can look for a pattern in how the terms relate to each other.
1. **Calculate the ratio of consecutive terms:**
- \( \frac{48}{16} = 3 \)
- \( \frac{144}{48} = 3 \)
- \( \frac{432}{144} = 3 \)
We see that each term is obtained by multiplying the previous term by 3.
2. **Expression for the nth term:**
- The first term \( a_1 = 16 \).
- The nth term in this geometric sequence can be expressed as:
\[
a_n = 16 \times 3^{n-1}
\]
Thus, the sequence is a **geometric sequence** with a first term of 16 and a common ratio of 3.
So, to conclude, this sequence is a geometric sequence.