1. SEQUENCES
Unit Standard
5248

2. Starter Write down the next three terms in the following sequences:-
2, 4, 6, 8, …, …, ….
3, 6, 12, 24, …, …, …
12, 7, 2, -3, …, …, …
8, 4, 2, 1, …, …, …
1, 3, 6, 10, …, …, …
2, -2, 2, -2, …, …, …

3. 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.

4. Arithmetic Sequences
An ARITHMETIC sequence is one where there is a common difference between terms.
Examples:-
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?

5. 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

6. 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

7. Arithmetic sequence examples
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
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

8. 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

9. 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.

10. Practice Examples Theta Maths Page 105 (Green) Exercise 13.1 Do q2,