To determine the next number in the sequence: 4, 12, 36, 108, let's analyze the pattern.
1. Identify the type of sequence:
The sequence appears to follow a pattern where each term is obtained by multiplying the previous term by a fixed number. This indicates that it is likely a geometric sequence.
2. Finding the common ratio:
- Calculate the ratio between consecutive terms:
- [tex]\( \frac{12}{4} = 3 \)[/tex]
- [tex]\( \frac{36}{12} = 3 \)[/tex]
- [tex]\( \frac{108}{36} = 3 \)[/tex]
The consistent ratio of 3 confirms that this sequence is geometric with a common ratio of 3.
3. Predict the next term:
- To find the next term in the sequence, multiply the last term by the common ratio:
- Last term: 108
- Common ratio: 3
- Next term: [tex]\( 108 \times 3 = 324 \)[/tex]
So, the next number in the sequence is:
A. 324
