A sequence is an ordered set of (usually) numbers .

In the context of sequences, what is a term ?

A term is one of the numbers in a sequence.

In the context of sequences, what is n ?

n is the position of a term in a sequence. E.g. when n = 3, it is referring to the third term of the sequence.

True or False? For the first term , n = 0.

False. For the first term, n = 1.

What is a position-to-term rule?

A position-to-term rule gives the n th term of a sequence as a formula in terms of n .

What is a term-to-term rule?

A term-to-term rule tells you how to find a term from the term before it. I.e., it gives the ( n +1)th term in terms of the n th term.

What is an arithmetic sequence ?

An arithmetic sequence is a sequence of numbers that increase or decrease by the same amount from one term to the next.

Define the common difference of an arithmetic sequence.

The common difference is the amount that an arithmetic sequence increases or decreases by from one term to the next.

What is an arithmetic series ?

An arithmetic series is where the terms of an arithmetic sequence are added together.

True or False? You need to know where the formula for the sum of an arithmetic series comes from.

False. You do not need to know where the sum of an arithmetic series formula comes from. You don't even need to remember the formula, as it is on the formula sheet at the front of the exam paper. You just need to know how to use it.

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FrontIntroduction to Sequences
What is a sequence?

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What is a sequence?
A sequence is an ordered set of (usually) numbers.
In the context of sequences, what is a term?
A term is one of the numbers in a sequence.
In the context of sequences, what is n?
n is the position of a term in a sequence.
E.g. when n = 3, it is referring to the third term of the sequence.
True or False?
For the first term, n = 0.
False.
For the first term, n = 1.
What is subscript notation for sequences?
Subscript notation is used to talk about a particular term.
For example
- $a_{1}$ is the 1st term
- $a_{7}$ is the 7th term
- $a_{n}$ is the nth term
What is a position-to-term rule?
A position-to-term rule gives the nth term of a sequence as a formula in terms of n.
How would you find the first three terms of a sequence using a position-to-term rule?
To find the first three terms of a sequence using a position-to-term rule, substitute $n = 1$ , $n = 2$ and $n = 3$ into the position-to-term formula.
What is a term-to-term rule?
A term-to-term rule tells you how to find a term from the term before it.
I.e., it gives the (n+1)th term in terms of the nth term.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers that increase or decrease by the same amount from one term to the next.
Define the common difference of an arithmetic sequence.
The common difference is the amount that an arithmetic sequence increases or decreases by from one term to the next.
What is $a$ the notation for in the context of arithmetic sequences and series?
$a$ is the notation for the first term in an arithmetic sequence (or series).
What is $d$ the notation for in the context of arithmetic sequences and series?
$d$ is the notation for the common difference of an arithmetic sequence (or series).
What is the position-to-term formula for an arithmetic sequence in terms of $a$ , $d$ and $n$ ?
The position-to-term formula for an arithmetic sequence in terms of $a$ , $d$ and $n$ is $a + (n - 1) d$ .
What is an arithmetic series?
An arithmetic series is where the terms of an arithmetic sequence are added together.
What is $S_{n}$ the notation for in the context of arithmetic sequences and series?
$S_{n}$ is the notation for the sum of the first n terms of an arithmetic series.
True or False?
You need to know where the formula for the sum of an arithmetic series comes from.
False.
You do not need to know where the sum of an arithmetic series formula comes from.
You don't even need to remember the formula, as it is on the formula sheet at the front of the exam paper.
You just need to know how to use it.
True or False?
You may be asked to find any one of $a$ , $d$ , $n$ or $S_{n}$ in a question.
True.
You may be asked to find any one of $a$ , $d$ , $n$ or $S_{n}$ in a question.
Always start by writing down which values you know and which one you are trying to find.

Numbers & the Number System

Equations, Formulae & Identities

Sequences, Functions & Graphs

Geometry & Trigonometry

Vectors & Transformation Geometry

Statistics & Probability