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# Term to term rule of a sequence

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## Mr Mattock

on 20 May 2016

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#### Transcript of Term to term rule of a sequence

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.

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.
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.
Examples
Key notes
Key notes
Key notes
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.

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
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
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
Full transcript