To solve the problem of finding the next number in the sequence [tex]\(100, 50, 25\)[/tex], let's carefully analyze the pattern.
1. Identify the pattern:
- Start with 100.
- The next number is 50, which is half of 100.
- Then, the next number is 25, which is half of 50.
2. Pattern recognition:
- From 100 to 50: [tex]\(50 = \frac{100}{2}\)[/tex]
- From 50 to 25: [tex]\(25 = \frac{50}{2}\)[/tex]
Thus, we can deduce that each number in the sequence is obtained by halving the previous number.
3. Apply the pattern to the next number:
- The last number in the sequence given is 25.
- Applying the same pattern, the next number is [tex]\( \frac{25}{2} \)[/tex].
4. Perform the division:
- [tex]\( \frac{25}{2} = 12.5 \)[/tex]
5. Verify against given options:
- (a) 5: This is not half of 25.
- (b) [tex]\(\frac{1}{5}\)[/tex]: This is not half of 25.
- (c) [tex]\(\frac{25}{2}\)[/tex]: This matches our calculated next number, which is 12.5.
Therefore, the correct choice for the next number in the sequence [tex]\(100, 50, 25\)[/tex] is:
[tex]\[ \boxed{\frac{25}{2}} \][/tex]
This answer aligns with choice (c).
