**Using Sequences**

What's the pattern?

1, 3, 9, 27, ....

Harder Pattern

3, ......, ......., 15.

**L.O. - Find missing terms in a sequence**

Identify the term to term rule for

a sequence.

Identify the term to term rule for

a sequence.

What's the pattern - part 2

9, 4, -1, ...., ....

What's the pattern?

What's the pattern - part 2

9, 4, -1, ..

-6

.., ..

-11

..

Harder Pattern

3, ...

7

..., ...

11

...., 15.

**Activities**

1, 3, 9, 27,

81, 243,

Geometric sequence - any sequence where you multiply by the same number to go from one term to the next.

with first term 1 and term to term rule of

'multiply by 3'

Arithmetic sequence - any sequence where you add the same number to go from one term to the next. Also called a linear sequence.

Start with 9 and subtract 5 (or add -5).

A linear sequence has first term of 3, and fourth term of 15. Fill in the missing terms.

A linear sequence has first term of 3, and fourth term of 15. Fill in the missing terms.

Start with 3 and add 4 each time.

**Examples**

**Key notes**

**Key notes**

**Key notes**

**Activity Answers**

Main Activity 1

Red

Find the next two terms and term to term rule for

these sequences.

(a) 5, 11, 17, 23, ...., ....

(b) 16, 9, 2, ...., ....

(c) 4, 16, 64, ....., .....

(d) 3, 15, 75, ...., .....

(e) 125, 25, 5, ...., .....

Amber

Find the missing terms in these sequences given the type of sequence.

(a) 5, ...., ....., 32 - Arithmetic

(b) 20, ....., ....., ......, 8 - Linear

(c) 1, ....., ......., 216 - Geometric

(d) 4, ....., ......, ......, 48 - Linear

(e) ....., ......, 2, ......, ....., -10 - Linear

Green

Find as many ways as you can to continue this sequence. For each, give the type of sequence (if you can) and the term to term rule you are using...

1, 2, 4, ...

Main Activity 1

Red

Find the next two terms and term to term rule for

these sequences.

(a) 5, 11, 17, 23,

29

,

35

(b) 16, 9, 2,

-5

,

-12

(c) 4, 16, 64,

256

,

1024

(d) 3, 15, 75,

375

,

1875

(e) 125, 25, 5,

1

,

Amber

Find the missing terms in these sequences given the type of sequence.

(a) 5,

14

,

23

, 32 - Arithmetic

(b) 20,

17

,

14

,

11

, 8 - Linear

(c) 1,

6

,

36

, 216 - Geometric

(d) 4,

15

,

26

,

37

, 48 - Linear

(e)

10

,

6

, 2,

-2

,

-6

, -10 - Linear

Green

Find as many ways as you can to continue this sequence. For each, give the type of sequence (if you can) and the term to term rule you are using...

1, 2, 4, ...

1

5

8, 16, 32... etc (Geometric, multiply by 2)

7, 11, 16, ... etc (Quadratic, goes up by the

next natural number)

6, 9, 12, 15, 19, ... (add 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 etc)

6, 10, 12, 16, ... (prime subtract 1)

Plenary

Design your own sequence, with a term to term rule.

Discuss on your table and choose your favourite sequence.

Design a 'missing terms' questions for your sequence (make sure you know the answer!)

Be prepared to solve other people's questions.

Starter

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

56 >> ÷2 , +12 , ÷ 5 , x12 , +4 , ÷ 4 , x3 , +6 , ÷9 ………….

8 >> x4 , ÷ 2 , -6 , double , ÷ 5 , +9 , x3 , x2 , ÷ 6 ………….

67 >> +5 , ÷ 8 , x10 , halve , -10 , ÷ 7 , x60 , ÷ 4 , -19 ………….

44 >> -8 , ÷ 4 , x6 , +2 , ÷ 4 , x3 , +18 , ÷ 2 , x6 ………….

64 >> ÷ 2 , +16 , ÷ 12 , square , x10 , -16 , ÷ 12 , x2 , ÷ 8 ………….

Starter

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

56 >> ÷2 , +12 , ÷ 5 , x12 , +4 , ÷ 4 , x3 , +6 , ÷9 …

9

.

8 >> x4 , ÷ 2 , -6 , double , ÷ 5 , +9 , x3 , x2 , ÷ 6 …

13

.

67 >> +5 , ÷ 8 , x10 , halve , -10 , ÷ 7 , x60 , ÷ 4 , -19 …

56

.

44 >> -8 , ÷ 4 , x6 , +2 , ÷ 4 , x3 , +18 , ÷ 2 , x6 …

180

.

64 >> ÷ 2 , +16 , ÷ 12 , square , x10 , -16 , ÷ 12 , x2 , ÷ 8 …

3

.