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Algebra 1

7.3.3 Quadratic Sequences

Algebra 17.3.3 Quadratic Sequences

7.3.3 Quadratic Sequences

7.3.3 • Quadratic Sequences

Activity

1.

Sketch the next step in the pattern. Explain what you sketched.

2.

Kiran says that the pattern is growing linearly because as the step number goes up by 1, the number of rows and the number of columns also increase by 1. Do you agree? Be prepared to show your reasoning.

3.

To represent the number of squares after nn steps, Diego and Jada wrote different equations. Diego wrote the equation f(n)=n(n+2)f(n)=n(n+2). Jada wrote the equation f(n)=n2+2nf(n)=n2+2n. Is either Diego or Jada correct? Be prepared to show your reasoning.

Video: Quadratic Sequences

Watch the following video to learn more about quadratic sequences.

Quadratic Sequences

Self Check

Which equation represents the relationship between the step number n and the number of squares y ?

  1. y = 2 n
  2. y = n 2 + 1
  3. y = n 2 + n
  4. y = n + 1

Additional Resources

More Complex Quadratic Patterns

See Steps 1 – 3 of a pattern of squares below. Write an equation representing the relationship between the step number nn and the number of squares yy.

First, try to find the pattern if the missing squares were actually there.

Make a table:

Step # of columns # of rows # of squares
1 2 2 2
2 2 2 7
3 4 4 14
nn n+1n+1 n+1n+1 (n+1)2−2(n+1)2−2

There would be (n+1)(n+1)(n+1)(n+1) squares, but there are 2 missing from each step, so the equation would be:

y=(n+1)2−2y=(n+1)2−2

Try it

More Complex Quadratic Patterns

See Steps 1 – 3 of a pattern of squares below. Write an equation representing the relationship between the step number nn and the number of squares yy.

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