What value will come in place of question mark (?) in the number series given below?
997, 961, 936, 920, 911, ?

Options

A. 901
B. 910
C. 905
D. 903

Answer

To find the value that will come in place of the question mark (?) in the series 997, 961, 936, 920, 911, we will analyze the pattern of differences between the consecutive numbers.

### Step-by-Step Solution:

1. **Identify the first number**: The first number in the series is 997.

2. **Calculate the difference between the first and second numbers**:
- \( 997 - 961 = 36 \)

3. **Calculate the difference between the second and third numbers**:
- \( 961 - 936 = 25 \)

4. **Calculate the difference between the third and fourth numbers**:
- \( 936 - 920 = 16 \)

5. **Calculate the difference between the fourth and fifth numbers**:
- \( 920 - 911 = 9 \)

6. **Summarize the differences**:
- The differences we have calculated are:
- \( 36, 25, 16, 9 \)

7. **Identify the pattern in the differences**:
- The differences are \( 6^2, 5^2, 4^2, 3^2 \) respectively:
- \( 36 = 6^2 \)
- \( 25 = 5^2 \)
- \( 16 = 4^2 \)
- \( 9 = 3^2 \)

8. **Continue the pattern**:
- The next difference should be \( 2^2 = 4 \).

9. **Subtract the next difference from the last number in the series**:
- \( 911 - 4 = 907 \)

10. **Conclusion**:
- Therefore, the value that will come in place of the question mark (?) is **907**.