Sequence notation | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these are the first 4 terms in the sequence with $n^\text{th}$ term rule $4n+2$ ?

2, 6, 10, 14, ...

4, 6, 8, 10, ...

6, 8, 10, 12, ...

6, 10, 14, 18, ... ✓
What is the correct $n^\text{th}$ term rule for the linear sequence which starts 2, 7, 12, 17, ...?

$2n + 7$

$2n + 5$

$5n -3$ ✓

$5n +2$
Match the first 4 terms of these sequences with possible term-to-term rules.

3, 5, 7, 9, ...

⇔

Start on 3, add 2 to the previous term to get the next term. ✓

3, 5, 9, 17, ...

⇔

Start on 3, double then subtract 1 to get the next term. ✓

3, 6, 9, 12, ...

⇔

Start on 3, add 3 to the previous term to get the next term. ✓

3, 6, 12, 24, ...

⇔

Start on 3, double the previous term to get the next term. ✓

3, 6, 15, 42, ...

⇔

Start on 3, subtract 1 then multiply by 3 to get the next term. ✓
What term number is 51 in the linear sequence which starts: 3, 9, 15, 21, ...?

the $8^\text{th}$ term

the $9^\text{th}$ term ✓

the $15^\text{th}$ term

the $16^\text{th}$ term

the $17^\text{th}$ term
A Fibonacci sequence starts 7, 11, 18, ... what is the fourth term?

'29' ✓
A Fibonacci sequence has first term 4 and fourth term 14. What is the second term?

'5' ✓

Which of these would be the correct notation to refer to the third term in a sequence?

$3n$

$3u$

$n_3$

$u_3$ ✓

$n^3$
Which of these could be correct notation for the linear sequence 5, 9, 13, 17, 21, ... ?

$u_{n} = u_{n+1} + 4, u_1 = 5$

$u_{n+1} = u_{n} + 4, u_1 = 5$ ✓

$u_{n} = u_{n+4}, u_1 = 5$

$u_{n} = u(n+4), u_1 = 5$
Match these terms to their rules.

4, 10, 22, 46, ..

⇔

$u_{n+1} = 2u_{n} + 2, u_1 = 4$ ✓

1, 5, 13, 29, ...

⇔

$u_{n+1} = 2u_{n} + 3, u_1 = 1$ ✓

1, 5, 17, 53, ...

⇔

$u_{n+1} = 3u_{n} + 2, u_1 = 1$ ✓

4, 12, 28, 60, ...

⇔

$u_{n+1} = 2(u_{n} + 2), u_1 = 4$ ✓
A linear sequence has $n^\text{th}$ term rule $5n +2$ which of these could describe the same sequence?

$u_{n+1} = u_{n} + 2 , u_1 = 5$

$u_{n+1} = u_{n} + 5 , u_1 = 2$

$u_{n+1} = u_{n} + 5 , u_1 = 7$ ✓

$u_{n+1} = 2u_{n} + 5 , u_1 = 2$

$u_{n+1} = 5u_{n} + 2 , u_1 = 7$
A sequence has rule $u_{n+2} = u_{n} + u_{n+1} , u_1 = 6, u_2 = 2$ . What is the $5^\text{th}$ term?

'18' ✓
A sequence has form $u_{n+1}= ku_n -3 , u_1 = 2$ If $u_3 = 6$ then $k= -\frac{3}{2}$ or $k=$ ______

'3' ✓

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Pupils may think that $u_1$ means that $u$ has a value of one.

$u_1$ refers to the first term in the sequence and $u_2$ refers to the second term. The subscript refers to the term number.

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.
Term-to-term - A term-to-term rule describes how to calculate the next term in the sequence from the previous term.
Fibonacci sequence - A Fibonacci sequence is a sequence where each term is the sum of the two previous terms.