What will come in place of question mark (?) in the given number series questions?
65 74 56 92 ? 164

Options

A. 25
B. 18
C. 24
D. 20

Answer

To solve the number series: 65, 74, 56, 92, ?, 164, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the Differences:**
- First, we calculate the differences between consecutive terms in the series.
- From 65 to 74:
\[ 74 - 65 = 9 \]
- From 74 to 56:
\[ 56 - 74 = -18 \]
- From 56 to 92:
\[ 92 - 56 = 36 \]

So far, we have the differences: +9, -18, +36.

2. **Analyze the Pattern of Differences:**
- The differences are alternating in sign: +, -, +.
- The absolute values of the differences are: 9, 18, 36.
- Notice that the second difference (18) is double the first (9), and the third difference (36) is double the second (18).

3. **Predict the Next Difference:**
- Following the pattern, the next difference should be double the last absolute difference (36):
\[ 36 \times 2 = 72 \]
- Since the pattern alternates in sign, the next difference will be negative:
\[ -72 \]

4. **Calculate the Missing Number:**
- The missing number (?) can be found by subtracting 72 from the last known number (92):
\[ ? = 92 - 72 = 20 \]

5. **Verify with the Next Term:**
- Now, we can check the next term in the series:
- From the missing number (20) to the final number (164):
\[ 164 - 20 = 144 \]
- This should be a positive difference, and we can see that it fits the pattern:
- The next difference should be +144, which is double the last negative difference (72).

### Final Answer:
The missing number in the series is **20**.