# Sequences, Series and Equations in Mathematics Free Course

• Description
• Outcome
• Certification
• This free online course is the second of our Upper-Secondary Mathematics suite of courses. It covers ratio and proportion, geometric sequences, arithmetic series, difference equations, linear programming, geometry, trigonometry, and graphs. This course is suitable for all math students revising for exams. It is also suitable for anyone with an interest in Mathematics.

• 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 right-angled 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.

• All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.

Having an official Alison document is a great way to share your success. Plus it’s:

• Ideal for including in CVs, job applications and portfolios
• An indication of your ability to learn and achieve high results
• An incentive to continue to empower yourself through learning
• A tangible way of supporting the Alison mission to empower people everywhere through education.

###### Modules List( 18 )
• 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)
• Arithmetic series
• Arithmetic series
• Finding the sum of an arithmetic series
• Finding the sum of an arithmetic sequence
• 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
• Difference equations 1
• Applications of sequences and series
• Making rungs for a ladder
• Growing Town
• 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
• 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
• Geometry
• Intersection of half planes
• Finding maximum and minimum values
• Solving linear and programming problems
• Solving linear programming problems - example
• Example part (b)
• 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
• Graphs
• Interpreting graphs
• Step graphs
• Distance-time graphs
• Power graphs
• Power graphs
• Linear representation of non-linear graphs
• Trigonometry 1
• Trigonometry introduction
• Right-angled triangles
• Solving non right-angled 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
• 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
• 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
• Ratio and proportion gears
• The gears video
• Further Maths Glossary
• Glossary
• Assessment
• Core Mathematics 2 Assessment
###### Topics List ( 10 )
Arithmetic sequences
Arithmetic Sequences This free online course covers topics related to arithmetic sequences.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 3 )
Arithmetic series
Arithmetic seriesThis free online course covers the arithmetic series.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 8 )
Geometric sequences
Geometric sequencesThis free online course covers topics related to geometric sequences.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 7 )
Geometric series
Geometric seriesThis free online course covers topics related to the geometric series.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 3 )
Difference equations 1
Difference equations 1This free online course covers topics related to difference equations.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 8 )
Difference equations 2
Difference equations 2This free online course covers topics related to difference equations.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 5 )
Difference equations 3
Difference equations 3This free online course covers topics related number patterns.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 5 )
Geometry
GeometryThis free online course covers topics related to geometry.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 15 )
Straight lines
Straight linesThis free online course covers topics related to the straight line.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 3 )
Graphs
GraphsThis free online course covers topics related to graphs such as time-distance graphs and step graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 2 )
Power graphs
Power graphsThis free online course is an introduction to the power graphs, and the linear representation of non-linear graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 10 )
Trigonometry 1
Trigonometry 1This free online course covers topics in trigonometry such as the sine rule and cosine rule.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 7 )
Trigonometry 2
Trigonometry 2 This free online course covers topics related to trigonometry, including surface area and volume, and Pythagoras' theorem. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 11 )
Pythagoras and bearings
Pythagoras and bearingsThis free online course is an introduction to topics related to Pythagoras.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 14 )
Ratio and proportion
Ratio and proportionThis free online course covers topics related to ratios and proportions.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 1 )
Ratio and proportion gears
Ratio and proportion gearsThis free online course contains a video relating to ratio and proportion gears.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
###### Topics List ( 1 )
Further Maths Glossary
Further Maths GlossaryThis free online course is a glossary for maths.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
Assessment
Assessment
##### Course Features
• Duration

3-4 Hours

• Publisher

XSIQ

• Video

Yes

• Audio

Yes

• Assessment

Yes

• Certification

Yes

• Price

Free

• Reward

50 Pts

• Responsive

No