**Sum of an Infinite Geometric Progression**

To find the sum of an infinite geometric progression (G.P.), we need to have a common ratio between the terms of the sequence. In this case, the common ratio can be found by dividing any term by its previous term.

The given G.P. sequence is as follows:
54, 18, 6, 2, ...

**Common Ratio**
To find the common ratio, we divide any term by its previous term:
18/54 = 1/3
6/18 = 1/3
2/6 = 1/3

Hence, the common ratio is 1/3.

**Infinite G.P. Formula**
The formula to find the sum of an infinite G.P. is given by:
S = a / (1 - r)

Where S is the sum of the infinite G.P., a is the first term, and r is the common ratio.

**Sum Calculation**
Now, we can substitute the values into the formula to find the sum:
S = 54 / (1 - 1/3)

To simplify the expression, we need to find a common denominator for the fraction:
S = 54 / (3/3 - 1/3)
S = 54 / (2/3)
S = 54 * (3/2)
S = 81

Hence, the sum of the infinite G.P. sequence 54, 18, 6, 2, ... is 81.

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