Question

Choose which expression can be used to determine the number ofsquares at stage n.4n - 25n - 32n^2n^2 + n

Answer 1

We are asked to find the expression that can be used to determine the number of squares at stage n.

At stage 1:

There are 2 squares

At stage 2:

There are 6 squares

At stage 3:

There are 12 squares

At stage 4:

There are 20 squares

Substitute n = 1,2,3,4 into each option and check which option satisfies the above number of squares.

Option 1:

`4n-2`

For n = 1:

4(1) - 2 = 4 - 2 = 2 (satisfied)

For n = 2:

4(2) - 2 = 8 - 2 = 6 (satisfied)

For n = 3:

4(3) - 2 = 12 - 2 = 10 (not satisfied)

Option 2:

`5n-3`

For n = 1:

5(1) - 3 = 5 - 3 = 2 (satisfied)

For n = 2:

5(2) - 3 = 10 - 3 = 7 (not satisfied)

Option 3:

`2n^2`

For n = 1:

2(1)^2 = 2(1) = 2 (satisfied)

For n = 2:

2(2)^2 = 2(4) = 8 (not satisfied)

Option 4:

`n^2+n`

For n = 1:

(1)^2 + 1 = 1 + 1 = 2 (satisfied)

For n = 2:

(2)^2 + 2 = 4 + 2 = 6 (satisfied)

For n = 3:

(3)^2 + 3 = 9 + 3 = 12 (satisfied)

For n = 4:

(4)^2 + 4 = 16 + 4 = 20 (satisfied)

Therefore, the correct answer is option 4.

The following expression can be used to determine the number of squares at stage n.

`n^2+n`

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