Quadratic sequences | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these could be the first 5 terms of a quadratic sequence?

5, 8, 12, 17, 23, ... ✓

8, 10, 14, 22, 38, ...

10, 14, 15, 13, 8, ... ✓

11, 20, 31, 51, 82, ...
Match the first 5 terms of these quadratic sequences to their common second differences.

-5, -3, 0, 4, 9, ...

⇔

common second difference of +1 ✓

-1, 7, 13, 17, 19, ...

⇔

common second difference of -2 ✓

4, 5, 8, 13, 20, ...

⇔

common second difference of +2 ✓

7, 11, 14, 16, 17, ...

⇔

common second difference of -1 ✓
Which is the correct $n^\text{th}$ term rule for the quadratic sequence which starts: 3, 6, 11, 18, 27, ...?

$n^2 -3$

$n^2 -2$

$n^2 -1$

$n^2 + 2$ ✓

$n^2 + 3$
The quadratic sequence which starts: 13, 16, 21, 28, ... has $n^\text{th}$ term rule $n^2 +$ ______

'12' ✓
What is the $n^\text{th}$ term of the linear sequence which starts -1, -2, -3, -4, ... ?

$1-2n$

$-n$ ✓

$n-1$

$n-2$

$n^2 -2$
What is the $n^\text{th}$ term of the linear sequence which starts -1, 2, 5, 8, ... ?

$-n + 3$

$3-4n$

$1-3n$

$3n -4$ ✓

$4n -3$

Which two sequences from the options below could be added to make the quadratic sequence which starts: 3, 7, 13, 21, ...?

$n^2: 1, 4, 9, 16, ...$ ✓

$2n^2: 2, 8, 18, 32, ...$

$-2n+3 : 1, -1, -3, -5, ...$

$n+1 : 2, 3, 4, 5, ...$ ✓

$3n-2: 1, 4, 7, 10, ...$
Which two sequences from the options below could be added to make the quadratic sequence which starts: 3, 7, 15, 27, ...?

$n^2: 1, 4, 9, 16, ...$

$2n^2: 2, 8, 18, 32, ...$ ✓

$-2n+3 : 1, -1, -3, -5, ...$ ✓

$n+1 : 2, 3, 4, 5, ...$

$3n-2: 1, 4, 7, 10, ...$
What is the correct $n^\text{th}$ term rule for the quadratic sequence which starts 3, 3, 5, 9, 15, ...?

$n^2 + 2$

$2n^2 + 1$

$n^2 -3n + 5$ ✓

$n^2 +3n-2$

$2n^2 -6n +7$
The $n^\text{th}$ term rule for the quadratic sequence 4, 9, 16, 25, ... is $n^2 +$ ______ $n + 1$

'2' ✓
What is the correct $n^\text{th}$ term rule for the quadratic sequence which starts -3, 1, 11, 27, 49, ... ?

$n^2 +n -5$

$3n^2 -5n -1$ ✓

$6n^2 -14n +5$

$12n^2 -32n+17$
What is the correct $n^\text{th}$ term rule for the quadratic sequence which starts -1, -6, -15, -28, -45, ... ?

$-2n^2 + n$ ✓

$-2n^2 - n + 2$

$-4n^2 - n - 2$

$-4n^2+ 7n - 4$

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Since there is no common difference, it is impossible to find the n^th term.

The first learning cycle shows how we can build quadratic sequences from n^2 and a linear sequence.

N^th term - The nth 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