**Sum of an Infinite Geometric Series**

An infinite geometric series is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant ratio. The sum of an infinite geometric series can be calculated using the formula:

S = a / (1 - r),

where S is the sum of the series, a is the first term, and r is the common ratio.

**Given Sequence**

The given sequence is 54, 18, 6, 2. To determine if it is a geometric sequence, we need to check if the ratio between consecutive terms is constant.

r = 18 / 54 = 1/3,
r = 6 / 18 = 1/3,
r = 2 / 6 = 1/3.

Since the ratio between consecutive terms is constant (1/3), the given sequence is indeed a geometric sequence.

**Finding the Sum**

In order to find the sum of the infinite geometric series, we need to know the first term (a) and the common ratio (r). In this case, the first term is a = 54 and the common ratio is r = 1/3.

Using the formula for the sum of an infinite geometric series:

S = a / (1 - r),

we can substitute the values:

S = 54 / (1 - 1/3).

Now, let's simplify the expression:

S = 54 / (2/3),
S = 54 * (3/2),
S = 81.

Therefore, the sum of the infinite geometric series 54, 18, 6, 2 is 81.

**Explanation**

- An infinite geometric series is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant ratio.
- The sum of an infinite geometric series can be calculated using the formula S = a / (1 - r), where S is the sum of the series, a is the first term, and r is the common ratio.
- To determine if a sequence is a geometric sequence, we need to check if the ratio between consecutive terms is constant.
- In the given sequence 54, 18, 6, 2, the ratio between consecutive terms is constant (1/3), indicating that it is a geometric sequence.
- By substituting the values of the first term (a = 54) and the common ratio (r = 1/3) into the formula, the sum of the infinite geometric series is calculated as 81.
- Therefore, the sum of the infinite geometric series 54, 18, 6, 2 is 81.