What should come in place of the question mark (?) in the following number series ?
(निम्नलिखित संख्या श्रृंखला में प्रश्नवाचक चिन्ह (?) के स्थान पर क्या आना चाहिए?)
`7" "8" "18" "?" "232" "1165`

Options

A. 84
B. 42
C. 57
D. 36

Answer

To find the missing number in the series: 7, 8, 18, ?, 232, 1165, we can analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the pattern**:
- The first number is 7.
- The second number is 8, which can be derived from the first number:
\[ 7 \times 1 + 1 = 8 \]

2. **Continue the pattern**:
- The third number is 18, which can be derived from the second number:
\[ 8 \times 2 + 2 = 16 + 2 = 18 \]

3. **Find the missing number**:
- To find the fourth number (the one represented by the question mark), we apply the same pattern:
\[ 18 \times 3 + 3 = 54 + 3 = 57 \]

4. **Verify the next number**:
- Now we check if this pattern holds for the next number, which is 232:
\[ 57 \times 4 + 4 = 228 + 4 = 232 \]
- This confirms that our derived number is correct.

5. **Final confirmation**:
- The next number after 232 should be:
\[ 232 \times 5 + 5 = 1160 + 5 = 1165 \]
- This also holds true.

Thus, the missing number in the series is **57**.