What should come in place of question mark (?) in the following number series ?
`10400" "2600" "650" "?" "40.625" "10.15625" "2.5390625`

Options

A. 185.5
B. 162.5
C. 164.75
D. 156.25

Answer

To find the missing number in the series `10400, 2600, 650, ?, 40.625, 10.15625, 2.5390625`, we can analyze the pattern of the numbers given.

1. **Identify the pattern**:
- Start with the first number: **10400**.
- The second number is **2600**.
- To find how we got from 10400 to 2600, we can divide 10400 by 4:
\[ 10400 \div 4 = 2600 \]

2. **Continue the pattern**:
- The third number is **650**.
- To find how we got from 2600 to 650, we again divide by 4:
\[ 2600 \div 4 = 650 \]

3. **Find the missing number**:
- Now we need to find the number that comes after 650. We will divide 650 by 4:
\[ 650 \div 4 = 162.5 \]
- Therefore, the missing number is **162.5**.

4. **Verify the next numbers**:
- The next number in the series is **40.625**.
- We can check if dividing 162.5 by 4 gives us 40.625:
\[ 162.5 \div 4 = 40.625 \]
- This confirms that our calculation is correct.

5. **Final check**:
- Continuing the pattern, we can check if dividing 40.625 by 4 gives us the next number, which is **10.15625**:
\[ 40.625 \div 4 = 10.15625 \]
- And finally, check if dividing 10.15625 by 4 gives us **2.5390625**:
\[ 10.15625 \div 4 = 2.5390625 \]
- All calculations confirm the pattern holds.

Thus, the number that should come in place of the question mark (?) is **162.5**.