What will come in place of question. Mark (?) in the following series questions?
9,64,25,216,?,512

Options

A. 49
B. 343
C. 81
D. 100

Answer

To solve the question, we need to identify the pattern in the given series: 9, 64, 25, 216, ?, 512.

**Step 1: Identify the numbers in the series.**
The numbers in the series are:
- 9
- 64
- 25
- 216
- ?
- 512

**Step 2: Recognize the mathematical operations.**
Let's analyze each number:
- 9 = \(3^2\) (3 squared)
- 64 = \(4^3\) (4 cubed)
- 25 = \(5^2\) (5 squared)
- 216 = \(6^3\) (6 cubed)
- 512 = \(8^3\) (8 cubed)

**Step 3: Identify the pattern.**
From the analysis, we can see a pattern:
- The series alternates between squares and cubes.
- The sequence of bases for squares is 3 and 5 (odd numbers).
- The sequence of bases for cubes is 4, 6, and 8 (even numbers).

**Step 4: Find the missing term.**
Following the established pattern, after 216 (\(6^3\)), the next term should be the square of the next odd number, which is 7:
- \(7^2 = 49\)

**Step 5: Conclude the answer.**
Thus, the number that will come in place of the question mark (?) is 49.

**Final Answer: 49**

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