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

Options

A. A)50
B. B)100
C. C)75
D. D)200

Answer

To find the missing term in the series: `?, 100, 150, 375, 1312.5`, we will analyze the pattern of multiplication between the terms.

### Step 1: Identify the pattern in the series
We have the following terms:
- Second term: 100
- Third term: 150
- Fourth term: 375
- Fifth term: 1312.5

Let's look at the multipliers between the terms:
- From 100 to 150:
\[ 150 = 100 \times 1.5 \]
- From 150 to 375:
\[ 375 = 150 \times 2.5 \]
- From 375 to 1312.5:
\[ 1312.5 = 375 \times 3.5 \]

### Step 2: Establish the pattern of multipliers
The multipliers we have identified are:
- 1.5 (from 100 to 150)
- 2.5 (from 150 to 375)
- 3.5 (from 375 to 1312.5)

We can see that the multipliers are increasing by 1 each time:
- The first multiplier is 1.5 (which can be represented as 1 + 0.5)
- The second multiplier is 2.5 (which can be represented as 2 + 0.5)
- The third multiplier is 3.5 (which can be represented as 3 + 0.5)

### Step 3: Find the multiplier for the first term
To find the first term (let's call it K), we need to determine the multiplier that would be applied to K to get the second term (100). Following the established pattern, the first multiplier should be:
\[ 0.5 \text{ (which is 0 + 0.5)} \]

### Step 4: Set up the equation
Now we can set up the equation:
\[ K \times 0.5 = 100 \]

### Step 5: Solve for K
To find K, we can rearrange the equation:
\[ K = \frac{100}{0.5} = 200 \]

### Conclusion
The missing term in the series is **200**.