563, 647, 479, 815, ?

Options

A. 672
B. 386
C. 279
D. 143

Explanation

To find the missing number in the series: 563, 647, 479, 815, ?, we can follow these steps:

### Step 1: Identify the differences between consecutive terms
- First, calculate the difference between the first two numbers:
\[ 647 - 563 = 84 \]
- Next, calculate the difference between the second and third numbers:
\[ 479 - 647 = -168 \]
- Then, calculate the difference between the third and fourth numbers:
\[ 815 - 479 = 336 \]

### Step 2: List the differences
Now we have the differences:
- First difference: \( +84 \)
- Second difference: \( -168 \)
- Third difference: \( +336 \)

### Step 3: Analyze the pattern in the differences
We can observe that:
- The first difference is \( 84 \)
- The second difference is \( -168 \) (which is \( -2 \times 84 \))
- The third difference is \( 336 \) (which is \( 4 \times 84 \))

### Step 4: Determine the next difference
Following the pattern, the next difference should be:
- \( -8 \times 84 \)

Calculating this:
\[ -8 \times 84 = -672 \]

### Step 5: Calculate the missing number
Now, we need to subtract this difference from the last known number in the series:
\[ 815 - 672 = 143 \]

### Conclusion
The missing number in the series is:
\[ \boxed{143} \]