Write the set `A = {1, 4, 9, 16 , 25 , dot dot dot }`in setbuilder form.

Explanation

To express the set \( A = \{1, 4, 9, 16, 25, \ldots\} \) in set-builder form, we need to identify a pattern or rule that governs the elements of the set.

### Step-by-Step Solution:

1. **Identify the Elements**: The elements of set \( A \) are \( 1, 4, 9, 16, 25, \ldots \). Observing these numbers, we can see that they are perfect squares.

2. **Determine the Pattern**: The elements can be expressed as:
- \( 1 = 1^2 \)
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