RESOURCE PACK 1

Topic: Sequences for Year 10/11

1 Starter Task Warmup – 10 questions on finding next 3 terms 8 mins

of a sequence. Increasing difficulty, answers
provided

2 Webpage notes and Notes on arithmetic, geometric, quadratic and 32 mins

questions special sequences

Flashcards, step by step solutions and

illustrations of sequences

Common misconception notes

Practice questions

3 Video 4 short Youtube videos on nth term sequences, 60 mins

geometric and Fibonacci sequences. Short
tutorial followed by guided worked solutions.

4 Worksheet Rich task – Don Steward – extending and 20 mins

generalising sequences (choice of two)

5 Timed Assessment Sequences Assessment – “full coverage” 55 mins

questions – one question from each style.
Answers provided

6 Extension Task Mixed worded questions – difficulty level high. 35 mins

Answers provided

Total time: 3h30m

Additional Guidance for pupils:

Task 1: Find the next three terms in each of the 10 sequences. Complete this task in 5
minutes then check your answers.

Task 2: Read this page entirely, and complete all of the questions/tasks included. Make use
of the step by step guides and in depth optional resources.

Task 3: Watch all the videos, completing the questions alongside the video.

Task 4: Select one of two worksheets from this task and try to incorporate all the ideas
showed so far.

Task 5: Complete this assessment in exam conditions.

Task 6: Attempt these tougher questions. They are longer, worded questions which are more
complex. Even if you do not reach a final answer, write out your working clearly.
Teacher Note:

This resource focuses on sequences. A starter task on 10 sequences refreshes students’

memory of this topic before getting into more in depth knowledge provided by the notesheet
in task two. Task three follows on with four videos that focus more closely on different types
of sequences, like the Fibonacci sequence, which students may find helpful and more
detailed. The rich task in task 4 stretch students by testing similar skills in a different context.
A timed assessment, which is full coverage, allows students to familiarise and try answering
one question from each style of question, before moving on to the extension task. The
extension task comprises more wordy questions, which can be challenging for some
students.

TASK ONE

TASK TWO

Click on the following link – read all notes and complete all questions

Sequences note sheet

TASK THREE

Click on the following links to the videos.

Quadratic Sequences

Nth Term

Fibonacci Sequences

Geometric Sequences
TASK FOUR - Pick ONE
TASK FIVE

"Full Coverage": Sequences

This worksheet is designed to cover one question of each type seen in past papers, for each
GCSE Higher Tier topic. This worksheet was automatically generated by the DrFrostMaths Homework

www.drfrostmaths.com/homework, logging on, Practise → Past Papers/Worksheets (or Library →

Platform: students can practice this set of questions interactively by going to

Past/Past Papers for teachers), and using the ‘Revision’ tab.

Question 1
Categorisation: Determine a term of a formula given the position-to-term formula.

[Edexcel GCSE(9-1) Mock Set 2 Spring 2017 1F Q24b, 1H Q7b] Here are
the first 7 terms of a quadratic sequence.

3 6 11 18 27 38 51

The 𝑛 th term of the sequence is 𝑛2 + 2 . (b) Find

the 50th term of the sequence.

..........................

Question 2
Categorisation: Determine an algebraic expression for a term of a sequence given a

term-to-term rule.

[Edexcel New SAMs Paper 3F Q20b, Paper 3H Q3b] Here are

the first six terms of a Fibonacci sequence.

1 1 2 3 5 8

The rule to continue a Fibonacci sequence is, the next term in the

sequence is the sum of the two previous terms

The first three terms of a different Fibonacci sequence are

𝑎 𝑏 𝑎+𝑏
Find the 6th term of this sequence, in terms of 𝑎 and 𝑏. Simplify your answer.

..........................

Question 3
Categorisation: Understand notation for term-to-term rules, i.e. if 𝒖𝒏 is the 𝒏th term of a
sequence, then 𝒖𝒏+𝟏 is the (𝒏 + 𝟏)th term.

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 3H Q17]

At the start of year , the quantity of a radioactive metal is 𝑃𝑛 At the start of the following year,
the quantity of the same metal is given by

𝑃𝑛+1 = 0.87𝑃𝑛

At the start of 2016 there were 30 grams of the metal.

What will be the quantity of the metal at the start of 2019? Give your
answer to the nearest gram.

.......................... grams

Question 4
Categorisation: Determine a formula for some aspect of a pictorial sequence.

[Edexcel IGCSE Jan2017-2F Q6e]

Here is a sequence of shapes drawn on a square grid.

The width of Shape number 1 is 3 squares.

The width of Shape number 2 is 4 squares.

The width of Shape number 𝑛 is 𝑊 squares. Write

down a formula for 𝑊 in terms of .
 𝑊 = ..........................

Question 5
Categorisation: Determine the 𝒏th term formula of an arithmetic/linear sequence.

[Edexcel GCSE Nov2006-3I Q10b, Nov2006-5H Q2a] Here are

the first five terms of a number sequence.

3 7 11 15 19

Write down an expression, in terms of 𝑛, for the 𝑛 th term of the number sequence.

..........................

Question 6
Categorisation: As above, but involving negative terms.

[Edexcel GCSE Nov2007-3I Q12bi, Nov2007-5H Q6bi Edited] Here are

the first five terms of a number sequence.

–4 –1 2 5 8

Find, in terms of 𝑛, an expression for the 𝑛 th term of this number sequence.

..........................

Question 7
Categorisation: Determine an expression for the (𝒏 + 𝟏)th term of a sequence given then
formula for the 𝒏th term.

[Edexcel IGCSE May2015-3H Q3b]

The first four terms of an arithmetic sequence are

5 9 13 17

The 𝑛 th term formula of this sequence is 4𝑛 + 1

Write down an expression, in terms of , for the (𝑛 + 1) th term.

..........................

Question 8
Categorisation: Determine when the 𝒏th term of two sequences is the same.

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 1F Q27] Here are

the first five terms of an arithmetic sequence.

2 7 12 17 22

The 𝑛 th term of a different arithmetic sequence is 4𝑛 + 15

The last term of each sequence is the same number.

There are the same number of terms in each sequence.

Find the number of terms in each sequence.

..........................

Question 9
Categorisation: Determine if a number occurs in a sequence.

[Edexcel GCSE Nov2006-5H Q2b Edited]

Here are the first five terms of a number sequence.

3 7 11 15 19

Adeel says that 319 is a term in the number sequence. Is

Adeel correct?
Question 10
Categorisation: As above, but for a descending sequence. [Edexcel

GCSE(9-1) Mock Set 3 Autumn 2017 2F Q8b Edited]

Here are the first five numbers in a sequence.

47 41 35 29 23

Sarah says,

“ –100 is not a number in this sequence.” Is

Sarah correct?

Question 11
Categorisation: As with Question 8, but the terms do not need to appear in the same
position.

[Edexcel GCSE Nov2007-3I Q12bii, Nov2007-5H Q6bii Edited]

Here are the first four terms of a number sequence.

2 7 12 17

Here are the first five terms of another number sequence.

–4 –1 2 5 8

Find two numbers that are in both number sequences.

..........................
Question 12
Categorisation: Find the 𝒏th term formula for a quadratic sequence.

[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 - 2H Q12a] Here are

the first four terms of a quadratic sequence.

3 8 15 24

Find an expression, in terms of 𝑛, for the 𝑛th term of this sequence.

..........................

Question 13
Categorisation: As above, but where the coefficient of the 𝒏 term is negative.

[Edexcel Specimen Papers Set 1, Paper 2H Q17]

Here are the first 5 terms of a quadratic sequence.

1 3 7 13 21

Find an expression, in terms of 𝑛, for the 𝑛 th term of this quadratic sequence.

..........................

Question 14
Categorisation: As above, but where the coefficient of 𝒏𝟐 is not 1.

[AQA IGCSE FM Practice paper set 3 P2 Q20] The first

five terms of a sequence are shown.

−1 2 9 20 35

Work out an expression for the 𝑛 th term of the sequence.

𝑛 th term = ..........................
Question 15
Categorisation: Determine the 𝒏th term of a quadratic sequence in a pictorial context.

[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 - 1H Q18]

The diagram shows the first 10 sides of a spiral pattern.

It also gives the lengths, in cm, of the first 5 sides.

The lengths, in cm, of the sides of the spiral form a sequence.

Find an expression in terms of 𝑛 for the length, in cm, of the 𝑛 th side.

..........................
Answers
Question 1
2502

Question 2
3𝑎 + 5𝑏

Question 3
20 grams

Question 4
𝑊=𝑛+2 Question 5
4𝑛 − 1 Question 6
3𝑛 − 7 Question 7
4𝑛 + 5

Question 8
18

Question 9
4𝑛 − 1 = 319
𝑛 = 80 ∴ Yes

Question 10
53 − 6𝑛 = −100
6𝑛 = 153 but 153 does not divide by 6. Therefore yes, not in sequence.

Question 11
Two of 2, 17, 32, 47, 62

Question 12
𝑛2 + 2𝑛

Question 13
𝑛2 − 𝑛 + 1
TASK SIX

Arithmetic Sequences – Mixed Problems

1. The first term of an arithmetic sequence is -8 and the common difference

is 3.

(a) Find the seventh term of the sequence.

(b) The last term is 100. How many terms are there?

2. There are 20 terms in an arithmetic sequence. The first term is -5 and the
last term is 90.

(a) Find the common difference.

(b) Find the sum of the terms in the sequence.

3. An arithmetic sequence is 120, 114, ……. , 36

(a) How many terms are there in the sequence?

(b) What is the sum of the terms in the sequence?

4. Matt Berry has a set of 12 stamps in his collection; the denominations

increase in steps of 2p starting with 1p.

(a) What is the highest denomination of stamp in the set?

(b) What is the total cost of the complete set?

5. Find the sum of all ODD numbers between 50 and 150.

6. The first term of an arithmetic sequence is 3000 and the tenth term is
1200.

(a) Find the sum of the first 20 terms of the sequence.

(b) After how many terms does the sum of the sequence become
negative?

7. Paul’s starting salary in a company is £14000 (because he did Maths!) and

during the time he stays with the company it increases by £500 per year.

(a) What is his salary in the sixth year?

(b) How many years has Paul been working for the company when his total
earnings for all his years there are £126,000?

8. The first three terms of an arithmetic series are (4x - 5), 3x and (x + 13).

(a) Find the value of x.

(b) Find the sum of the first 40 terms of the sequence.

9. A jogger is training for a 10km charity run. He starts with a run of 400m,
then he increases the distance he runs by 200m per day.

(a) How many days does it take the jogger to reach a distance of 10km?

(b) What total distance will he have run in training by then?

EXTENSION

10. The fifth term in an arithmetic sequence is 28 and the tenth term is 58.

(a) Find the first term and the common difference.

(b) The sum of all the terms is 444. How many terms are there?

11. The training programme of a pilot requires him to fly ‘circuits’ of an

airfield. Each day he flies 3 more circuits than the day before. On the fifth
day he flew 14 circuits.
 Calculate how many circuits he flew:

(a) On the first day

(b) In total by the end of the fifth day

(c) In total by the end of the nth day

(d) In total from the end of the nth day to the end of the 2nth day. Simplify
your answer.

12. The sum of the first four terms of an arithmetic series is 96. The sum of
the fifth, sixth and seventh terms is 219.

(a) Find the first term and common difference.

(b) Find and simplify an expression in terms of n for the sum of the first n
terms of the series.

Arithmetic Sequences – Mixed Problems Answers

1) (a) 10

(b) 37

2) (a) 5

(b) 850

3) (a) 15

(b) 1170

4) (a) 23p

(b) £1.44

5) 5000

6) (a) 22000
 (b) 17th is the first negative term. 32 terms for sum to be negative

7) (a) £16500

(b) 8

8) (a) 8

(b) -1260

9) (a) 49

(b) 254.8km

10) (a) a=4, d=6

(b) 12

11) (a) 2

(b) 40

n
( 3 n+1)
(c) 2

n
( 9 n+1)
(d) 2

2
12) (a) a=3, d=14 (b) 7 n −4 n
END OF PACK