Write a rule for the pattern below. Use $x$ to represent the step number (instead of $n$ ).
Assume the first step is step 1.

Answer

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Answer

$\boxed{f(x) = x^2}$

Steps

Step 1 ：Observe the sequence: [1, 4, 9, 16, 25]

Step 2 ：Notice the differences between consecutive terms: [3, 5, 7, 9]

Step 3 ：The differences increase by 2 each time, indicating a quadratic function of the form $ax^2 + bx + c$

Step 4 ：Using the first three terms, find the coefficients a, b, and c

Step 5 ：The rule for the pattern is $f(x) = x^2$

Step 6 ：$\boxed{f(x) = x^2}$