To solve the problem, we need to understand the sequence given and then find the value of \( A \) that satisfies the condition \( 14 < A < 20 \).

The sequence provided is:
\[ A = \frac{2}{1.4} / 3.6 / 5.8 / 7 / \ldots / 200 / 199 \]

First, let's simplify the first term:
\[ \frac{2}{1.4} = \frac{2}{1.4} = \frac{2}{\frac{14}{10}} = \frac{2 \times 10}{14} = \frac{20}{14} = \frac{10}{7} \]

So the sequence starts with:
\[ A = \frac{10}{7} / 3.6 / 5.8 / 7 / \ldots / 200 / 199 \]

The sequence appears to be a product of fractions of the form \( \frac{n}{n-1} \) for \( n = 2, 3.6, 5.8, 7, \ldots, 200 \).

However, the sequence given is not entirely clear in its pattern, especially with the non-integer values like 3.6 and 5.8. To proceed, let's assume the sequence is a product of fractions where each term is of the form \( \frac{n}{n-1} \).

If we consider the sequence as:
\[ A = \frac{2}{1} \times \frac{3.6}{2.6} \times \frac{5.8}{4.8} \times \frac{7}{6} \times \ldots \times \frac{200}{199} \]

We need to find the value of \( A \) that lies between 14 and 20.

Given the complexity of the sequence, let's approximate it by considering the general behavior of such a product. For large \( n \), the product of terms like \( \frac{n}{n-1} \) tends to grow logarithmically.

However, without a clear pattern or more information, it's challenging to provide an exact value for \( A \).

Given the condition \( 14 < A < 20 \), we can infer that the product of the sequence lies within this range.

Therefore, the value of \( A \) that satisfies the condition \( 14 < A < 20 \) is an approximation based on the given sequence.

To get a precise value, we would need to compute the product explicitly, which is complex due to the non-integer terms. However, based on the given condition, we can conclude that \( A \) is within the range \( 14 < A < 20 \).