What will be come in place of the question mark (?) in the given number series
19 20 16 25 9 ?

Options

A. 45
B. 55
C. 59
D. 34

Answer

To find the missing number in the series: 19, 20, 16, 25, 9, ?, we can analyze the pattern of the numbers.

1. **Identify the Pattern:**
- The series alternates between increasing and decreasing numbers.
- The first number is 19, then it increases to 20.
- Next, it decreases to 16.
- Then it increases to 25.
- Finally, it decreases to 9.

2. **Calculate the Changes:**
- From 19 to 20: Increase by 1 (which is \(1^2\)).
- From 20 to 16: Decrease by 4 (which is \(2^2\)).
- From 16 to 25: Increase by 9 (which is \(3^2\)).
- From 25 to 9: Decrease by 16 (which is \(4^2\)).

3. **Continue the Pattern:**
- The next operation should be an increase, following the established pattern.
- The next increase should be by \(5^2 = 25\).

4. **Calculate the Missing Number:**
- Start from the last number in the series, which is 9.
- Add \(25\) to \(9\):
\[ 9 + 25 = 34 \]

5. **Conclusion:**
- The missing number in the series is **34**.

Thus, the answer is **34**.