1, 9, 25, 49, ? , 121

Options

A. 64
B. 81
C. 91
D. 100

Explanation

To find the missing number in the series: 1, 9, 25, 49, ?, 121, we can follow these steps:

### Step 1: Identify the pattern in the series
The numbers in the series are 1, 9, 25, 49, and 121. We can look for a pattern among these numbers.

### Step 2: Recognize the numbers as perfect squares
We can express these numbers as perfect squares:
- 1 = \(1^2\)
- 9 = \(3^2\)
- 25 = \(5^2\)
- 49 = \(7^2\)
- 121 = \(11^2\)

### Step 3: Identify the odd numbers
From the above, we can see that the numbers whose squares are given are odd numbers:
- 1 (from \(1^2\))
- 3 (from \(3^2\))
- 5 (from \(5^2\))
- 7 (from \(7^2\))
- 11 (from \(11^2\))

### Step 4: Find the missing number
The odd numbers in sequence are 1, 3, 5, 7, and the next odd number is 9. Therefore, the missing number in the series is:
- 9 = \(9^2 = 81\)

### Conclusion
Thus, the missing number in the series is **81**.

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