What will come in place of question mark (?) in the following series questions?
21,22,?,35,51,76

Options

A. A)28
B. B)23
C. C)24
D. D)26

Answer

To find the missing term in the series 21, 22, ?, 35, 51, 76, we will analyze the differences between the consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Identify the given series**:
The series is: 21, 22, ?, 35, 51, 76.

2. **Calculate the differences between the known consecutive terms**:
- From 21 to 22:
\[ 22 - 21 = 1 \]
- From 35 to 51:
\[ 51 - 35 = 16 \]
- From 51 to 76:
\[ 76 - 51 = 25 \]

3. **List the differences we have**:
- The difference from 21 to 22 is **1**.
- The difference from 35 to 51 is **16**.
- The difference from 51 to 76 is **25**.

4. **Recognize the pattern in the differences**:
- The differences we have so far are: **1, ?, 16, 25**.
- Notice that 1 is \(1^2\), 16 is \(4^2\), and 25 is \(5^2\).
- We can infer that the missing difference (from 22 to ?) should be \(2^2 = 4\) and the difference from ? to 35 should be \(3^2 = 9\).

5. **Calculate the missing term**:
- Starting from 22, if we add the missing difference (4):
\[ ? = 22 + 4 = 26 \]
- To confirm, we can also check the next term:
\[ 26 + 9 = 35 \]
- This confirms our calculation is correct.

6. **Final answer**:
The missing term in the series is **26**.