What will come in place of question mark (?) inthe following number series'
3 123 183 213 228 235.5 ?

Options

A. 238.25
B. 239.25
C. 275.5
D. 238.5

Answer

To find the missing number in the series \(3, 123, 183, 213, 228, 235.5, ?\), we will analyze the differences between the consecutive numbers.

### Step 1: Calculate the differences between the numbers
1. From \(3\) to \(123\):
\[ 123 - 3 = 120 \]
2. From \(123\) to \(183\):
\[ 183 - 123 = 60 \]
3. From \(183\) to \(213\):
\[ 213 - 183 = 30 \]
4. From \(213\) to \(228\):
\[ 228 - 213 = 15 \]
5. From \(228\) to \(235.5\):
\[ 235.5 - 228 = 7.5 \]

### Step 2: Identify the pattern in the differences
The differences we calculated are:
- \(120\)
- \(60\)
- \(30\)
- \(15\)
- \(7.5\)

We can see that each difference is half of the previous difference:
- \(120\) is halved to get \(60\)
- \(60\) is halved to get \(30\)
- \(30\) is halved to get \(15\)
- \(15\) is halved to get \(7.5\)

### Step 3: Calculate the next difference
Following the pattern, the next difference should be half of \(7.5\):
\[ \frac{7.5}{2} = 3.75 \]

### Step 4: Add this difference to the last number in the series
Now, we will add this difference to the last number \(235.5\):
\[ 235.5 + 3.75 = 239.25 \]

### Conclusion
Thus, the number that will come in place of the question mark (?) is:
\[ \boxed{239.25} \]

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