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Answer:  n^2 + 1

Explanation:

Imagine that you cross out the top-most square for each step of each diagram. The squares not crossed out have the following counts: 1, 4, 9

This is the sequence of perfect squares. So the rule will have us take the number n, and square it to get n^2. Then we add on the squares we crossed out earlier. This explains the "plus 1" at the end to get the answer of n^2+1

Answer:

[tex] {n}^{2} + 1 \\ \: respresents \: the \: following \: \\ function[/tex]

i hope it helped.

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