**Term to term rule of a sequence**

Starter

What's the pattern?

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

Harder Pattern

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

**L.O. - Understand the types of sequence and**

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, -6, ....

What's the pattern?

What's the pattern - part 2

9, 4, -1, -6, ...

Harder Pattern

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

**Activities**

1, 3, 9, 27,

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. Find the term to term rule.

A linear sequence has first term of 3, and fourth term of 15. Find the term to term rule of the sequence.

Start with 3 and add 4 each time.

**Examples**

**Key notes**

**Key notes**

**Key notes**

**Activity Answers**

Main Activity 1

Red

Find the

term to term rule

for

these sequences.

(a)

5, 11, 17, 23, ....

(b)

16, 9, 2, -5, ....

(c)

4, 16, 64, 256, ....

(d)

3, 15, 75, 365, ....

(e)

125, 25, 5, 1, ...

.

Amber

Find the

term to term rule

of these sequences given the type of sequence.

(a)

5, ...., ....., 32 - Arithmetic

(b)

20, ....., ....., ......, 8 - Linear

(c)

4, ....., ......, ......, 48 - Linear

(d)

....., ......, 2, ......, ....., -10 - Linear

(e)

1, ....., ......., 216 - Geometric

Green

(a) A sequence starts with these numbers:

Say what the next term is if the sequence is

linear

and

why

.

2, 6, ...

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.

+ 12

+ 4

+ 4

+ 4

(b) The sequence is actually

geometric

. State what the

next term

would be and what the

term to term rule

is.

(c) If these were the first two terms in a Fibonacci-style sequence, what would the next three terms be?

(d) How many different

quadratic sequences

can you find that start

with these two terms?

Main Activity 1

Red

Find the

term to term rule

for

these sequences.

(a)

Start at 5 and add 6

(b)

Start at 16 and subtract 7

(c)

Start at 4 and times by 4

(d)

No rule

(e)

Start at 125 and times by

Amber

Find the

term to term rule

of these sequences given the type of sequence.

(a)

Start at 5 and add 9

(b)

Start at 20 and subtract 3

(c)

Start at 4 and add 11

(d)

Start at 10 and subtract 4

(e)

Start at 1 and multiply by 6

Green

2, 6, ...

1

5

(a)

Linear - 10, rule start at 2 and add 4

(b)

Geometric - 18, rule start at 2 and multiply by 3

(c) Quadratics

2, 6, 11, 17

or

2, 6, 12, 20

, or

2, 6, 13, 23

, etc

A sequence goes up by 5 every time.

Explain why it is impossible to write down this sequence.

A sequence starts at 4 and goes up by 5 every time.

Write down the first 4 terms of this sequence

Starter

A sequence goes up by 5 every time.

Explain why it is impossible to write down this sequence - because there are infinitely many sequences that go up by 5 every time.

A sequence starts at 4 and goes up by 5 every time.

Write down the first 4 terms of this sequence -

4, 9, 14, 19, ...

What's the pattern - part 3

5, 4, 6, 11, 19, ....

What's the pattern - part 3

5, 4, 6, 11, 19, ....

-1 +2 +5 +8

+3 +3 +3

Quadratic - second difference the same each time.

**Key notes**

What's the pattern - part 4

1, 1, 2, 3, 5, 8, 13, ...

What's the pattern - part 4

1, 1, 2, 3, 5, 8, 13, ...

Fibonacci(-style) sequence - each term is the sum of the previous two terms.

Start with 1 and 1 as the first two terms and then add the previous two terms to get the next one.

**Key notes**