Download sequences - Nayland Maths

SEQUENCES
Unit Standard
5248
Starter

Write down the next three terms in
the following sequences:1)
2)
3)
4)
5)
6)
2, 4, 6, 8, …, …, ….
3, 6, 12, 24, …, …, …
12, 7, 2, -3, …, …, …
8, 4, 2, 1, …, …, …
1, 3, 6, 10, …, …, …
2, -2, 2, -2, …, …, …
Definition

Simply speaking a sequence is an ordered
list of numbers.

Every sequence has a first number, a
second number, etc

For most sequences there is a rule which
can tell us what each number should be.

The numbers in a sequence are known as
terms.
Arithmetic Sequences


An ARITHMETIC sequence is one
where there is a common difference
between terms.
Examples:a)
b)
c)
d)
e)
1, 2, 3, 4, …..
3, 5, 7, 9, ……
10, 15, 20, 25, …..
0, 0.5, 1, 1.5, 2, 2.5, …..
3, 0, -3, -6, …… In each example, can you see
what the common difference is?
Notation

Any term in a sequence is written as
tn, where the n refers to the position in
the sequence.
Eg:-

t3 is the third term,
t5 is the fifth term
The first term is also referred to as a
ie a = t1
Notation for an Arithmetic
Sequence
In an arithmetic sequence the
common difference is d.
 Examples:




1, 4, 7, 10, ….
a=1, d=3
10, 8, 6, 4, ….
a=10, d=-2
5, 11, 17, 23, ….
a=5, d=6
1.73, 1.87, 2.01, 2.15,
a=1.73,
d=0.14
Arithmetic sequence
examples

i.
ii.
iii.
iv.
v.
Given a and d list the
first 5 terms.
a=1, d=4
a=7, d=-6
a=-95, d=3
a=13, d=11
a=1.5, d=0.75
i.
ii.
iii.
iv.
v.
1, 5, 9, 13, 17
7, 1, -5, -11, -17
-95, -92, -89, -86, -83
13, 24, 35, 46, 57
1.5, 2.25, 3.0, 3.75,
4.5
A formula for the terms of an
Arithmetic sequence.




The first term of an arithmetic sequence is :a
To get the second term add on the d.
t2 = a + d
To get the third term add another d.
t3 = a + d + d
= a + 2d
The fourth term will be..
t4 = t3 +d
= a + 2d + d
= a + 3d
General term for an Arithmetic
Sequence

Any term in an arithmetic sequence can be
found using the formula:
tn = a + (n – 1)d


Example: If a = 5 and d = 2 then
t100 = 5 + (100-1).2
= 203
tn is known as the general term or the nth
term of the sequence.
Practice Examples

Theta Maths
(Green)
Do
Page 105
Exercise 13.1
q2,
q3,
q5,
q10,
q11