Explanation

The pattern of the series appears to be square numbers:

• 1 = 1^2
• 9 = 3^2
• 25 = 5^2
• 49 = 7^2
• 81 = 9^2
• 121 = 11^2

So, the correct completion of the series would be:

1, 9, 25, 49, 81, 121