What will come in place of question mark (? ) in the following number series ?
निम्नलिखित संख्या श्रंखला में प्रश्नवाचक चिन्ह (?) के स्थान पर क्या आयेगा ?
`39" "52" "78" "117" "169" "?`

Options

A. 246
B. 182
C. 234
D. 256

Answer

To find the missing number in the series `39, 52, 78, 117, 169, ?`, we will analyze the pattern of the differences between consecutive numbers.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 39, 52, 78, 117, 169.

2. **Calculate the differences between consecutive terms**:
- Difference between 52 and 39:
\[ 52 - 39 = 13 \]
- Difference between 78 and 52:
\[ 78 - 52 = 26 \]
- Difference between 117 and 78:
\[ 117 - 78 = 39 \]
- Difference between 169 and 117:
\[ 169 - 117 = 52 \]

3. **List the differences**: The differences we calculated are:
- 13, 26, 39, 52

4. **Observe the pattern in differences**: The differences are increasing and can be expressed as:
- 13 (which is \(1 \times 13\))
- 26 (which is \(2 \times 13\))
- 39 (which is \(3 \times 13\))
- 52 (which is \(4 \times 13\))

5. **Predict the next difference**: Following the established pattern, the next difference should be:
- \(5 \times 13 = 65\)

6. **Add the next difference to the last term in the series**:
- Add 65 to the last term (169):
\[ 169 + 65 = 234 \]

7. **Conclusion**: The number that comes in place of the question mark (?) is **234**.

### Final Answer:
The missing number in the series is **234**.