What is A23: Sequences?

A term-to-term rule produces each new term from the preceding term or terms, so begin with every stated starting value and apply the operations in the given order.

How many marks are A23 questions worth?

In verified past-paper appearances, A23 questions on Edexcel GCSE Maths 1MA1 have been worth 1–6 marks.

Which past exam papers has A23 appeared in?

A23 has appeared in 18 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

A23

Generate terms of a sequence from either a term-to-term or a position-to-term rule

Sequences

Worked answers, methods and verified real exam appearances for A23 on Edexcel GCSE Maths 1MA1.

Explanation

A term-to-term rule produces each new term from the preceding term or terms, so begin with every stated starting value and apply the operations in the given order.
A position-to-term rule gives a term directly from its position $n$ ; for the first terms substitute $n=1,2,3,\ldots$ unless the question explicitly defines another starting index.
Multi-step, alternating and Fibonacci-type rules require intermediate terms to be shown because a later term may depend on more than one earlier value.
The examiner expects the terms in order and usually gives method credit for correct substitutions or repeated operations even if a later arithmetic error occurs.

Worked example

A sequence starts $2,5$ . Each later term is one more than the sum of the previous two terms. Find the next three terms.

1.Third term: $2+5+1=8$ .
2.Fourth term: $5+8+1=14$ .
3.Fifth term: $8+14+1=23$ .

Answer: $8,14,23$ .

Common mistakes

Don't substitute $n=0$ for the first term when the sequence starts at $n=1$ .
Don't repeatedly use the original starting pair instead of the latest two terms for a two-term recurrence.

Exam tip

Write each intermediate term because a correct recurrence method can still earn marks after one arithmetic slip.

Worked practice

Tier 1 · Easy

A sequence has position-to-term rule

6n-2

. Write down its first four terms.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$4,10,16,22$	2	Substitute $n=1,2,3,4$ into $6n-2$ . This gives $4$ , $10$ , $16$ and $22$ .

Tier 2 · Standard

A sequence starts

2,5

. Each later term is one more than the sum of the previous two terms. Write down the next three terms.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$8,14,23$	3	The third term is $2+5+1=8$ . The fourth is $5+8+1=14$ . The fifth is $8+14+1=23$ .

Tier 3 · Hard

The

n

th term of a sequence is

n^2-3n+4

. Generate the first six terms.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$2,2,4,8,14,22$	4	Substitute $n=1$ through $6$ : $1-3+4=2$ , $4-6+4=2$ , $9-9+4=4$ , $16-12+4=8$ , $25-15+4=14$ and $36-18+4=22$ .

Tier 1 · Easy

A sequence starts with

7

. The term-to-term rule is multiply by

2

and then subtract

3

. Write down the next two terms.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$11,19$	2	The second term is $7\times2-3=11$ . Apply the rule again: $11\times2-3=19$ .

Tier 2 · Standard

A sequence begins

4,7,13,22

. The amounts added are

3,6,9

and continue in the same pattern. Write down the next two terms.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$34,49$	2	The next amount added is $12$ , giving $22+12=34$ . Then add $15$ , giving $34+15=49$ .

Tier 3 · Hard

A sequence starts

3,8

. Each later term is three times the previous term minus the term before that. Write down the next three terms.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$21,55,144$	3	The third term is $3(8)-3=21$ . The fourth is $3(21)-8=55$ . The fifth is $3(55)-21=144$ .

Tier 2 · Standard

A sequence starts with

6

. To get successive terms, alternately add

5

and multiply by

2

, beginning by adding

5

. Write down the next five terms.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$11,22,27,54,59$	3	Starting from $6$ , add $5$ to get $11$ , multiply by $2$ to get $22$ , add $5$ to get $27$ , multiply by $2$ to get $54$ , then add $5$ to get $59$ .

Tier 3 · Hard

A sequence is defined by

u_n=n^2+2

when

n

is odd and

u_n=3n-1

when

n

is even. Write down the first eight terms. Work out

u_{11}-u_{10}

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$3,5,11,11,27,17,51,23$ $u_{11}-u_{10}=94$	4	Use $n^2+2$ at odd positions and $3n-1$ at even positions. This gives $3,5,11,11,27,17,51,23$ . Also $u_{11}=11^2+2=123$ and $u_{10}=3(10)-1=29$ , so the difference is $123-29=94$ .

Tier 3 · Hard

A sequence starts with

60

. If a term is even, the next term is found by dividing it by

2

. If a term is odd, the next term is found by adding

7

. Write down the next six terms.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$30,15,22,11,18,9$	3	$60$ is even, so the next term is $30$ ; $30$ is even, giving $15$ ; $15$ is odd, giving $22$ ; $22$ is even, giving $11$ ; $11$ is odd, giving $18$ ; and $18$ is even, giving $9$ .

Q10

Tier 3 · Hard

A sequence satisfies

u_{n+1}=2u_n+n

for

n\ge1

. Given that

u_5=74

, work backwards to find

u_1

u_2

u_3

and

u_4

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$u_1=3$ , $u_2=7$ , $u_3=16$ , $u_4=35$	4	Reverse the rule at each position. From $u_5=2u_4+4$ , $u_4=(74-4)/2=35$ . Then $u_3=(35-3)/2=16$ , $u_2=(16-2)/2=7$ and $u_1=(7-1)/2=3$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2021-11	1F	Q13	3	Non-calculator	Foundation	QP MS
2022-06	1F	Q9	2	Non-calculator	Foundation	QP MS
2019-06	2F	Q28	3	Allowed	Foundation	QP MS
2024-11	1F	Q2	1	Non-calculator	Foundation	QP MS
2023-06	2F	Q9	3	Allowed	Foundation	QP MS
2024-11	2H	Q15	6	Allowed	Higher	QP MS
2022-11	2F	Q3	1	Allowed	Foundation	QP MS
2019-11	2H	Q6	3	Allowed	Higher	QP MS
2023-11	3F	Q8	4	Allowed	Foundation	QP MS
2022-11	3F	Q10	2	Allowed	Foundation	QP MS
2022-11	2F	Q20	4	Allowed	Foundation	QP MS
2022-11	2H	Q3	4	Allowed	Higher	QP MS
2022-06	3F	Q8	2	Allowed	Foundation	QP MS
2022-06	3H	Q20	4	Allowed	Higher	QP MS
2019-06	3F	Q13	2	Allowed	Foundation	QP MS
2019-11	3F	Q8	2	Allowed	Foundation	QP MS
2019-11	2F	Q26	3	Allowed	Foundation	QP MS
2024-06	3H	Q17	3	Allowed	Higher	QP MS

Other points in A Algebra · sequences and functions

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