Transcript Numbers - Toynbee School

Algebra
th
n
Term
Algebra
When we are working to
th
find the n term we are
looking to find patterns
in number sequences.
Algebra
Look at this sequence of
numbers:
5, 9, 13, 17, 21, 25,
…, 29,
…,
What are the next two
numbers in the sequence?
Algebra
th
10
What would the
number
be?
5, 9, 13, 17, 21, 25,
…, 29,
…,
How can we know without
the 8th and 9th numbers..?
Algebra
We need to be able to use the
‘place’ value of each number
th
(the n term)
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
Algebra
Now look at each number in
the sequence.
What is the difference
between each number?
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
4 4 4 4 4 4
Algebra
This difference tells us how
much we need to multiply the
th
n term by.
1x 4= 4
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
4 4 4 4 4 4
Algebra
But the sequence number is
5, not 4!
OK, then just add 1 as well
1 x 4 = 4 4 +1= 5
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
4 4 4 4 4 4
Algebra
We know n has to be
multiplied by 4, add 1
Now try it on another n… 6?
6 x 4 = 24 24 +1= 25
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
4 4 4 4 4 4
Algebra
So our rule for finding any
number in this sequence is…
4n + 1
1 2 3 4 5 6 7
5, 9, 13, 17, 21, 25, 29
4 4 4 4 4 4
Algebra
When answering a question
is it really important to
present it so that it is really
clear. Draw a small table to
show both the sequence
and the term place values…
Algebra
nth term
Sequence
Difference
1
2
2
5
3
3
8
3
4 5 6 7
11 14 17 20
3
3 3 3
Difference between numbers is 3
Term 1 is multiplied by 3 then subtract 1 = 2
= 3n-1
4th term
4 x 3 - 1 = 11