112 119 140 175 224 (?)

Options

A. 277
B. 276
C. 287
D. 266

Explanation

To find the missing number in the series: 112, 119, 140, 175, 224, (?), we can follow these steps:

### Step 1: Identify the differences between consecutive terms
- The difference between 112 and 119 is:
\[ 119 - 112 = 7 \]
- The difference between 119 and 140 is:
\[ 140 - 119 = 21 \]
- The difference between 140 and 175 is:
\[ 175 - 140 = 35 \]
- The difference between 175 and 224 is:
\[ 224 - 175 = 49 \]

### Step 2: List the differences
The differences we found are:
- 7
- 21
- 35
- 49

### Step 3: Analyze the pattern in the differences
Now, let's look at the differences:
- 7 can be expressed as \(7 \times 1\)
- 21 can be expressed as \(7 \times 3\)
- 35 can be expressed as \(7 \times 5\)
- 49 can be expressed as \(7 \times 7\)

We can see that the differences are increasing by odd numbers:
- The first difference is \(7 \times 1\)
- The second difference is \(7 \times 3\)
- The third difference is \(7 \times 5\)
- The fourth difference is \(7 \times 7\)

### Step 4: Determine the next difference
Following the pattern, the next difference should be:
- \(7 \times 9 = 63\)

### Step 5: Add the next difference to the last term
Now, we add this difference to the last term in the series:
\[ 224 + 63 = 287 \]

### Conclusion
Thus, the missing number in the series is **287**.

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