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The figure shows the first three in a sequence of squares. The first square in the sequence has a side length of 3 units, and each square after that has a side length that is 2 units longer than the previous square.What is the explicit equation for f (n) that represents the areas of the squares in the sequence? f (n) = 2(n − 1)2 + 3 f (n) = (3 + 2(n − 1))2 f (n) = (3 + 2n)2 f (n) = 3n2

The figure shows the first three in a sequence of squares The first square in the sequence has a side length of 3 units and each square after that has a side le class=

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SOLUTION:

Since the sequence of side lengths are;

[tex]3,3+2n,3+4n,...[/tex]

Their areas would be the sequence;

[tex]9,(3+2n)^2,(3+4n)^2,...[/tex]

Thus, the explicit formula for the area is;

[tex]f(n)=(3+2(n-1))^2[/tex]

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