63, 31, 15, 7, 3, ?

Options

A. 0
B. 1
C. 2
D. 3

Explanation

To find the missing number in the series 63, 31, 15, 7, 3, ?, we can analyze the pattern of the series step by step.

### Step 1: Identify the pattern
We observe that the numbers are decreasing rapidly. This suggests that there might be a consistent operation applied to each number to get to the next.

**Hint:** Look for a mathematical operation that connects each number to the next.

### Step 2: Analyze the first two numbers (63 to 31)
To go from 63 to 31, we can express this as:
\[ 31 = \frac{63 - 1}{2} \]
This means we subtract 1 from 63 and then divide by 2.

**Hint:** Check if the same operation applies to the next pairs of numbers.

### Step 3: Analyze the second pair (31 to 15)
Using the same operation:
\[ 15 = \frac{31 - 1}{2} \]
Again, we subtract 1 from 31 and divide by 2.

**Hint:** Confirm if this pattern holds for the next pairs.

### Step 4: Analyze the third pair (15 to 7)
Continuing with the pattern:
\[ 7 = \frac{15 - 1}{2} \]
We subtract 1 from 15 and divide by 2.

**Hint:** Keep following this pattern to see if it holds true for the next numbers.

### Step 5: Analyze the fourth pair (7 to 3)
Now, we apply the same operation:
\[ 3 = \frac{7 - 1}{2} \]
Subtracting 1 from 7 and dividing by 2 gives us 3.

**Hint:** Now, apply the same operation to find the next number.

### Step 6: Find the missing number (3 to ?)
To find the next number after 3, we apply the same operation:
\[ ? = \frac{3 - 1}{2} \]
Calculating this gives:
\[ ? = \frac{2}{2} = 1 \]

### Conclusion
Thus, the missing number in the series is **1**.

**Final Answer:** The missing number is **1**.