In each series missing term is mentioned by question mark (?). Find out the missing term in given alternatives and write its alternative number against the correct question number on your answer sheet-
1, 4, ?, ?, 125, 36,?

Options

A. 27, 16, 49
B. 9, 16, 49
C. 27, 64, 49
D. 27, 16, 343

Answer

To solve the series 1, 4, ?, ?, 125, 36, ?, we need to identify the pattern in the sequence.

### Step-by-step Solution:

1. **Identify the Known Terms**:
The known terms in the series are:
- 1 (which is \(1^3\))
- 4 (which is \(2^2\))
- 125 (which is \(5^3\))
- 36 (which is \(6^2\))

2. **Recognize the Pattern**:
We can see that the series alternates between cubes of odd numbers and squares of even numbers:
- The first term is \(1^3\) (odd)
- The second term is \(2^2\) (even)
- The third term should be \(3^3\) (odd)
- The fourth term should be \(4^2\) (even)
- The fifth term is \(5^3\) (odd)
- The sixth term is \(6^2\) (even)
- The seventh term should be \(7^3\) (odd)

3. **Calculate the Missing Terms**:
- The third term (odd number) is \(3^3 = 27\).
- The fourth term (even number) is \(4^2 = 16\).
- The seventh term (odd number) is \(7^3 = 343\).

4. **Compile the Complete Series**:
Thus, the complete series is:
- 1, 4, 27, 16, 125, 36, 343.

5. **Identify the Missing Terms**:
- The first missing term is 27.
- The second missing term is 16.
- The third missing term is 343.

### Final Answer:
The missing terms in the series are:
- 1st missing term: 27
- 2nd missing term: 16
- 3rd missing term: 343