Introducing quadratic sequences | Maths | Quizalize & Oak National Academy

Starter quiz

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

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

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

3, -6, -15, -24, ... ✓

3, -6, -3, -9, ...
Here is part of the sequence of square numbers: ... 49, 64, 81, 100, ... What is the common second difference for this sequence?

'2' ✓
What is the $10^\text{th}$ term in the sequence with $n^\text{th}$ term rule $5n - 6$ ?

'44' ✓
Which of these are examples of quadratic expressions?

$3x + 4$

$x^2$ ✓

$2^x + 5$

$4x-3x^2$ ✓

$x^3 + x^2$
In the sequence with $n^\text{th}$ term rule $4n-2$ which term has the value 46?

The $11^\text{th}$ term

The $12^\text{th}$ term ✓

The $21^\text{st}$ term

The $25^\text{th}$ term

46 is not in the sequence $4n-2$
The sequence of all square numbers starts 1, 4, 9, ... what is the $20^\text{th}$ term in this sequence?

'400' ✓

Exit quiz

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

'205' ✓
What is the $8^\text{th}$ term in the sequence with $n^\text{th}$ term rule $n^2 - 2n$ ?

'48' ✓
Match up the first 5 terms in these quadratic sequences with the correct common second difference.

-3,0, 1, 0, -3, ...

⇔

common second difference -2 ✓

2, 4, 8, 14, 22, ...

⇔

common second difference 2 ✓

3, 4, 9, 18, 31, ...

⇔

common second difference 4 ✓

4, 10, 17, 25, 34, ...

⇔

common second difference 1 ✓

10, 8, 9, 13, 20, ...

⇔

common second difference 3 ✓

12, 16, 19, 21, 22, ...

⇔

common second difference -1 ✓
Match up the first 5 terms in these sequences with a possible sequence type.

1, 2, 4, 8, 16, ...

⇔

geometric ✓

2, 3, 5, 8, 12, ...

⇔

quadratic ✓

3, 7, 11, 15, 19, ...

⇔

arithmetic ✓

4, 6, 10, 16, 26, ...

⇔

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

$n^2 -9$ ✓

$n^2 -8$

$n^3 +3$

$n^2 + 8$

$n^2 + 9$
What is the $10^\text{th}$ term in the quadratic sequence which starts 18, 21, 26, 33, 42, ...?

'117' ✓

Worksheet

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Lesson Details

Key learning points

A quadratic sequence does not have a common difference.
The second differences between terms are equal.

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.

Keywords

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