Calculus and Above

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Assume the following pattern with...

Assume the following pattern with terms built of square tile figures continues and complete parts (a) through (c) below.

A figure consists of 2 equal sized squares in a column.

A figure consists of 5 equal sized squares. In the center is a column of 3 squares. From the bottom square, 1 more square extends to the left. From the top square, 1 more square extends to the right.

A figure consists of 8 equal sized squares. In the center is a column of 4 squares. From the bottom square, 2 more squares extend to the left. From the top square, 2 more squares extend to the right.

A figure consists of 11 equal sized squares. In the center is a column of 5 squares. From the bottom square, 3 more squares extend to the left. From the top square, 3 more squares extend to the right.

a. How many square tiles are there in the seventh figure?

nothing

b. How many square tiles are in the nth figure?

A.

There are 3nplus1 square tiles in the nth figure.

B.

The figures do not appear to follow any predictable pattern.

C.

There are 3n square tiles in the nth figure.

D.

There are 3 n minus 1 square tiles in the nth figure.

c. Is there a figure that has exactly 488 square tiles? If so, which one? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

Yes. Figure number

nothing has 488 square tiles.

B.

No. There does not exist a figure with exactly 488 square tiles.

A figure consists of 2 equal sized squares in a column.

A figure consists of 5 equal sized squares. In the center is a column of 3 squares. From the bottom square, 1 more square extends to the left. From the top square, 1 more square extends to the right.

A figure consists of 8 equal sized squares. In the center is a column of 4 squares. From the bottom square, 2 more squares extend to the left. From the top square, 2 more squares extend to the right.

A figure consists of 11 equal sized squares. In the center is a column of 5 squares. From the bottom square, 3 more squares extend to the left. From the top square, 3 more squares extend to the right.

a. How many square tiles are there in the seventh figure?

nothing

b. How many square tiles are in the nth figure?

A.

There are 3nplus1 square tiles in the nth figure.

B.

The figures do not appear to follow any predictable pattern.

C.

There are 3n square tiles in the nth figure.

D.

There are 3 n minus 1 square tiles in the nth figure.

c. Is there a figure that has exactly 488 square tiles? If so, which one? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

Yes. Figure number

nothing has 488 square tiles.

B.

No. There does not exist a figure with exactly 488 square tiles.

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