Question
What kind of sequence is this?
12, 36, 108, 324, ...
12, 36, 108, 324, ...
Answers
Answered by
GPT-4o mini
The given sequence is 12, 36, 108, 324, ...
To determine what kind of sequence it is, we can look at how each term relates to the previous term.
1. The second term (36) is obtained from the first term (12) by multiplying by 3:
\[
12 \times 3 = 36
\]
2. The third term (108) is obtained from the second term (36) by multiplying by 3:
\[
36 \times 3 = 108
\]
3. The fourth term (324) is obtained from the third term (108) by multiplying by 3:
\[
108 \times 3 = 324
\]
Thus, each term in the sequence can be described as:
- \( a_1 = 12 \)
- \( a_n = a_{n-1} \times 3 \) for \( n > 1 \)
This means each term is 3 times the previous term. Therefore, this is a geometric sequence where each term is multiplied by a common ratio of 3.
In summary, the sequence is a **geometric sequence** with a first term of 12 and a common ratio of 3.
To determine what kind of sequence it is, we can look at how each term relates to the previous term.
1. The second term (36) is obtained from the first term (12) by multiplying by 3:
\[
12 \times 3 = 36
\]
2. The third term (108) is obtained from the second term (36) by multiplying by 3:
\[
36 \times 3 = 108
\]
3. The fourth term (324) is obtained from the third term (108) by multiplying by 3:
\[
108 \times 3 = 324
\]
Thus, each term in the sequence can be described as:
- \( a_1 = 12 \)
- \( a_n = a_{n-1} \times 3 \) for \( n > 1 \)
This means each term is 3 times the previous term. Therefore, this is a geometric sequence where each term is multiplied by a common ratio of 3.
In summary, the sequence is a **geometric sequence** with a first term of 12 and a common ratio of 3.