What value will come in place of question mark (?) in the number-series given below?
13 58.5 204.75 ? 767.8125

Options

A. 512.775
B. 511.875
C. 511.375
D. 511.275

Answer

To solve the problem of finding the missing value in the series: 13, 58.5, 204.75, ?, 767.8125, we can analyze the pattern of multiplication between the numbers.

### Step-by-step Solution:

1. **Identify the first two terms:**
- The first term is 13.
- The second term is 58.5.

2. **Calculate the multiplication factor from the first term to the second term:**
\[ \text{Factor} = \frac{58.5}{13} = 4.5 \]

3. **Identify the second and third terms:**
- The second term is 58.5.
- The third term is 204.75.

4. **Calculate the multiplication factor from the second term to the third term:**
\[ \text{Factor} = \frac{204.75}{58.5} = 3.5 \]

5. **Identify the pattern of multiplication factors:**
- The factors we have so far are 4.5 and 3.5.
- It appears that the factors are decreasing by 1 for each step.

6. **Determine the next multiplication factor:**
- Following the pattern, the next factor should be 2.5.

7. **Calculate the missing term using the third term and the next factor:**
\[ \text{Missing term} = 204.75 \times 2.5 = 511.875 \]

8. **Identify the fourth and fifth terms:**
- The fourth term is 511.875.
- The fifth term is 767.8125.

9. **Calculate the multiplication factor from the fourth term to the fifth term:**
\[ \text{Factor} = \frac{767.8125}{511.875} = 1.5 \]

10. **Confirm the pattern:**
- The factors are: 4.5, 3.5, 2.5, and 1.5, which confirms the decreasing pattern.

### Conclusion:
The value that will come in place of the question mark (?) is **511.875**.

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