N^th term - The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.
Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 When x is the variable, they have general form ax^2 + bx + c

Common misconception

Since there is no common difference, further terms in the sequence cannot be generated.

Pupils have seen sequences where the first difference is not common and seen examples of other rules. In this lesson, the concept of a second difference is introduced and this can be used to generate the next first difference.

The first learning cycle focuses on generating and identifying quadratic sequences. This recaps substituting and squaring a value. This learning cycle can be condensed if you feel your pupils do not need as much practice.

Teacher tip

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This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Which of these could be the first 4 terms in an arithmetic sequence?

3, -6, 12, -24, ...

3, -6, -12, -15, ...

Correct answer: 3, -6, -15, -24, ...

3, -6, -3, -9, ...

Q2.

Here is part of the sequence of square numbers: ... 49, 64, 81, 100, ... What is the common second difference for this sequence?

Correct Answer: 2, +2

Q3.

What is the $$10^\text{th}$$ term in the sequence with $$n^\text{th}$$ term rule $$5n - 6$$?

Correct Answer: 44

Q4.

Which of these are examples of quadratic expressions?

$$3x + 4$$

Correct answer: $$x^2$$

$$2^x + 5$$

Correct answer: $$4x-3x^2$$

$$x^3 + x^2$$

Q5.

In the sequence with $$n^\text{th}$$ term rule $$4n-2$$ which term has the value 46?

The $$11^\text{th}$$ term

Correct answer: The $$12^\text{th}$$ term

The $$21^\text{st}$$ term

The $$25^\text{th}$$ term

46 is not in the sequence $$4n-2$$

Q6.

The sequence of all square numbers starts 1, 4, 9, ... what is the $$20^\text{th}$$ term in this sequence?

Correct Answer: 400

Exit quiz

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6 Questions

Q1.

What is the $$10^\text{th}$$ term in the sequence with $$n^\text{th}$$ term rule $$2n^2 + 5$$?

Correct Answer: 205

Q2.

What is the $$8^\text{th}$$ term in the sequence with $$n^\text{th}$$ term rule $$n^2 - 2n$$?

Correct Answer: 48

Q3.

Match up the first 5 terms in these quadratic sequences with the correct common second difference.

Correct Answer:-3,0, 1, 0, -3, ...,common second difference -2

common second difference -2

Correct Answer:2, 4, 8, 14, 22, ...,common second difference 2

common second difference 2

Correct Answer:3, 4, 9, 18, 31, ...,common second difference 4

common second difference 4

Correct Answer:4, 10, 17, 25, 34, ...,common second difference 1

common second difference 1

Correct Answer:10, 8, 9, 13, 20, ...,common second difference 3

common second difference 3

Correct Answer:12, 16, 19, 21, 22, ...,common second difference -1

common second difference -1

Q4.

Match up the first 5 terms in these sequences with a possible sequence type.

Correct Answer:1, 2, 4, 8, 16, ...,geometric

geometric

Correct Answer:2, 3, 5, 8, 12, ...,quadratic

quadratic

Correct Answer:3, 7, 11, 15, 19, ...,arithmetic

arithmetic

Correct Answer:4, 6, 10, 16, 26, ...,Fibonacci

Fibonacci

Q5.

Which is the correct $$n^\text{th}$$ term rule for the quadratic sequence which starts: -8, -5, 0, 7, 16, ...?

Correct answer: $$n^2 -9$$

$$n^2 -8$$

$$n^3 +3$$

$$n^2 + 8$$

$$n^2 + 9$$

Q6.

What is the $$10^\text{th}$$ term in the quadratic sequence which starts 18, 21, 26, 33, 42, ...?

Correct Answer: 117