Final answer:
The sequence is a geometric progression where each term is half the previous one, making the next number in the sequence 12.
Step-by-step explanation:
To find the next number in the sequence 192, 96, 48, 24, we need to identify the pattern that the sequence follows. In this sequence, each number is half the previous number. This is a common mathematical sequence called a geometric progression, where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
In this case, the common ratio is 0.5 (or ½), because we are consistently halving each term to get to the next one. Starting with 192 and continuously multiplying by 0.5, the sequence progresses as follows:
- 192 × 0.5 = 96
- 96 × 0.5 = 48
- 48 × 0.5 = 24
- 24 × 0.5 = 12
Therefore, the next number in the sequence is 12. If we continue this pattern, we can find subsequent numbers as well, simply by continuing to halve each new term we calculate.
This exploration represents an application of basic arithmetic and an understanding of sequences in mathematics, specifically within the category of geometric sequences, which is a fundamental topic covered in many middle school math curricula.