Sequence or not ... That's the question.

Clearly, the first 3 terms (1,4,9) and 121 are squares. So that gives us a hint that the middle numbers should also be squares. If we read the numbers from right to left, then, it would be 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 ... So the next term should be 441 (144 reading from the write).

Take the number position, then evaluate its square, finally read it backward.

The sequence consist of the reverses of square numbers. 1, 4, 9 stay the same. 16 becomes 61. 25 becomes 52. 36 becomes 63. So on. The next number in the sequence is the reverse of the square of 12, which is 144 -> 441.

1^{2} = 1 2^{2} = 4 3^{2} = 9 4^{2} = 16, reversing this : 61 5^{2} = 25 => 52 . . . . . 11^{2} = 121 => 121 12^{2} = 144 => 441

Flip each number, and you will get the following:

1, 4, 9, 16, 25, 36, 49....

and it is clear that this pattern is that of the square of successive integers.

we are left of with 11 squared (121), so the next value must be 12 squared, which is 144. Flip 144 and you get 441, which is the answer.

Each of the numbers in the set corresponds to the next square, only it's digits are inverted - so 'xyz' becomes 'zyx'. After isolating each number and realizing that the order of the squares is increasing linearly, the next square - or the twelfth number - can be assumed to be '12'. 12^2 = 144. So it becomes 441.

1X1=1,2X2=4,.........4X4=16 but in invert form its 61..........similarly for 12..... its square is 144 and its inverse is 441