What will come in the place of question (?) mark in following number series:
`?," "100," "150," "375," "1312.5`

Options

A. 100
B. 200
C. 150
D. 400

Answer

To find the missing number in the series: `?, 100, 150, 375, 1312.5`, we will analyze the pattern in the series starting from the known numbers.

### Step 1: Identify the pattern
Let's look at the numbers we have: 100, 150, 375, and 1312.5. We will check the ratios or the differences between consecutive terms.

### Step 2: Calculate the ratios
1. **From 100 to 150:**
\[ \text{Ratio} = \frac{150}{100} = 1.5 \]

2. **From 150 to 375:**
\[ \text{Ratio} = \frac{375}{150} = 2.5 \]

3. **From 375 to 1312.5:**
\[ \text{Ratio} = \frac{1312.5}{375} = 3.5 \]

### Step 3: Identify the pattern in the ratios
The ratios we calculated are:
- From 100 to 150: 1.5
- From 150 to 375: 2.5
- From 375 to 1312.5: 3.5

We can see that the ratios are increasing by 1:
- 1.5 (first ratio)
- 2.5 (second ratio, which is 1.5 + 1)
- 3.5 (third ratio, which is 2.5 + 1)

### Step 4: Calculate the ratio for the missing term
Following the pattern, the ratio before 1.5 should be:
\[ 1.5 - 1 = 0.5 \]

### Step 5: Calculate the missing term
Now we can find the missing term (let's denote it as \( x \)):
\[ x \times 1.5 = 100 \]
To find \( x \):
\[ x = \frac{100}{1.5} = \frac{1000}{15} = \frac{200}{3} \approx 66.67 \]

### Conclusion
Thus, the missing number in the series is approximately \( 66.67 \).

### Final Answer
The missing number is \( \frac{200}{3} \) or approximately \( 66.67 \).

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