Sequences, Series and Equations in Mathematics
Gain a better understanding of series and equations, cuboid, Hamilton circuit and path, Prim's algorithm, and more!
Description
This course begins by teaching you about arithmetic sequences. You will learn that an arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same. You will then study arithmetic series as well as geometric sequences and series. This course will then discuss the intersection of halfplanes and show you how to solve linear and programming problems. You will also look into graphs, power graphs, and the linear representation of nonlinear graphs.
You will then learn about Pythagoras who is a Greek mathematician who developed a theorem to find the length of the third side of a triangle. This course will also discuss the angle of elevation and depression, directions and bearings, contour maps, traverse surveys, compass bearings, and true bearings. You will look into ratio and proportion where you will learn that a ratio is a comparison between two like quantities in the same units. In addition, you will study ratio and proportion gears.
Upon the completion of this course, you will be able to calculate sequences and sequences, find the equation of a straight line, and know how to interpret graphs effectively. You will also better understand the positive and negative gradient in straight line graphs. This course will also ensure you gain a better insight into rightangled triangles, area of a triangle, the sine rule, cosine rule, Pythagoras' theorem, surface area, and volume so make sure to check out this course and enhance your math skills!
Modules
Arithmetic series
Further Maths Glossary
Difference equations 1
Difference equations 2

Difference equations

Generating a sequence from a difference equation

Difference equations that represent arithmetic sequences

Difference equations that represent geometric sequences

Generate the first 4 terms of a sequence

Generate the first 4 terms of another sequence

Find a general expression for the nth term

Find a general expression for the nth term
Geometric sequences

Geometric sequences

Is this a geometric sequence?

Find a term in an increasing geometric sequence

Find a term in a decreasing geometric sequence

Which term has that value?

Example (b)

Example (c)

Example (d)
Geometric series

Geometric series

Infinite geometric series

Find the sum of an increasing geometric sequence

Find the sum of a decreasing geometric sequence

How many terms until the sum exceeds 2000?

Find the sum of an infinite geometric series

Sum a geometric series to infinity
Geometry

Intersection of half planes

Finding maximum and minimum values

Solving linear and programming problems

Solving linear programming problems  example

Example part (b)
Graphs
Difference equations 3

Other first order difference equations

Solving difference equations

Find a general expression for the nth term

Find the first term from a given term

Find the first term from the second term
Power graphs
Pythagoras and bearings

The tomb of Pythagoras activity

Angles of elevation and depression

Directions and bearings

Contour maps

Traverse surveys

Compass bearings

True Bearings

Bearings application example

Field survey example

Field survey example continued

Bearings yachting example
Ratio and proportion gears
Ratio and proportion

Ratio and proportion

Simplifying ratios

Expressing ratios as a percentage

Dividing quantities in a given ratio

Applications of ratio and proportion

Map scales

Dilution factors

Photography

Gears

Finding x values in ratios

Map scales: how far is that?

Dilution: drug strength

Photographing a tree

Gearing up... gearing down
Arithmetic sequences

Arithmetic sequences

Find a particular term in an arithmetic sequence

How many terms in this arithmetic sequence?

Show that the sequence is arithmetic

Solving arithmetic sequences simultaneously

Summing up arithmetic sequences

Is this an arithmetic sequence?

Example (b)

Example (c)

Example (d)
Straight lines

Straight line graphs

The general equation of a straight line

Finding the equation of a line

Simultaneous equations

Method 1  elimination

Method 2  substitution

Sketching linear equations

Break even analysis

Straight line graphs  gradient

Finding the gradient given the coordinates of two points

Elimination examples

The break even example

Sketching linear equations  example 1

Sketching linear equations  example 2

Straight line graphs  gradient example
Trigonometry 1

Trigonometry introduction

Rightangled triangles

Solving non rightangled triangles

The sine rule

The cosine rule

The area of a triangle

Example

Example 2

Cosine rule – Example 1

Cosine rule – Example 2
Trigonometry 2

Pythagoras' theorem

Pythagoras in 3 dimensions

Similar figures

Surface area and volume

Similar figures example

Surface area and volume: example 1

Surface area and volume: example 2
Assessment
Learning Outcomes
On completing of this course you will be able to calculate arithmetic sequences, geometric sequences, geometric series, difference equations and more successfully. You will understand the positive and negative gradient in straight line graphs. You will be able to find the equation of a straight line and know how to interpret graphs effectively. You will gain a good knowledge of trigonometry such as rightangled triangles, area of a triangle, the sine rule, cosine rule, Pythagoras' theorem, surface area, and volume. You will know how to simplify ratios and much more.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
Ideal for sharing with potential employers  include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Certificates for completed Certificate courses:
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