The next number of the sequence is `1/2,3/4,5/8,7/16` is

Options

A. `10/24`
B. `11/32`
C. `9/24`
D. `9/32`

Answer

To find the next number in the sequence \( \frac{1}{2}, \frac{3}{4}, \frac{5}{8}, \frac{7}{16} \), we can analyze the pattern in both the numerators and the denominators.

### Step 1: Identify the pattern in the numerators
The numerators of the fractions are:
- 1 (from \( \frac{1}{2} \))
- 3 (from \( \frac{3}{4} \))
- 5 (from \( \frac{5}{8} \))
- 7 (from \( \frac{7}{16} \))

We can see that the numerators form an arithmetic sequence where each term increases by 2:
- \( 1 + 2 = 3 \)
- \( 3 + 2 = 5 \)
- \( 5 + 2 = 7 \)

Thus, the next numerator will be:
- \( 7 + 2 = 9 \)

### Step 2: Identify the pattern in the denominators
The denominators of the fractions are:
- 2 (from \( \frac{1}{2} \))
- 4 (from \( \frac{3}{4} \))
- 8 (from \( \frac{5}{8} \))
- 16 (from \( \frac{7}{16} \))

We can observe that the denominators are powers of 2:
- \( 2^1 = 2 \)
- \( 2^2 = 4 \)
- \( 2^3 = 8 \)
- \( 2^4 = 16 \)

Following this pattern, the next denominator will be:
- \( 2^5 = 32 \)

### Step 3: Combine the results
Now that we have both the next numerator and denominator, we can form the next term in the sequence:
- Next term = \( \frac{9}{32} \)

### Final Answer
Thus, the next number in the sequence is \( \frac{9}{32} \).

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