Write the set A = \{1, 4, 9, 16, 25, . . . \} in set-builder form.

Answer: $A = \{x \mid x = n^2, n \in \mathbb{N}\}$

Step-by-step solution

Step 1: Identify the pattern

Observe the elements of the given set $A$ . We can see that each element is the square of a natural number. The first element is $1^2$ , the second is $2^2$ , the third is $3^2$ , and so on.

Step 2: Define the general term

Based on the observed pattern, we can represent any element $x$ in the set as the square of a natural number $n$ . Here, $n$ belongs to the set of natural numbers, denoted by $\mathbb{N} = \{1, 2, 3, . . . \}$ .

Step 3: Write in set-builder form

Using the general term, we can write the set $A$ in set-builder form. This notation means 'the set of all $x$ such that $x$ is equal to $n^2$ , where $n$ is a natural number'.

Write the set A = \{1, 4, 9, 16, 25, . . . \} in set-builder form.

Step-by-step solution

Step 1: Identify the pattern

Step 2: Define the general term

Step 3: Write in set-builder form

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