AS Maths Masterclass. Lesson 1: Arithmetic series. Learning objectives. The student should be able to: recognise an Arithmetic Progression (AP); recall the formula for the sum to n terms; evaluate the terms and sum of a given AP; manipulate formulae that model APs.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
The student should be able to:
5 + 7 + 9 + 11 + 13 + … … + 29
– 8 – 5 – 2 + 1 + 4
40 + 30 + 20 + 10 + 0 – 10 – 20 – 30 – 40
E.g. Take 5 + 7 + 9 + 11 + … + 29
Each term is bigger than its previous term by 2
We have that
And further that
Click here for weblink 2
Click here for spreadsheet
If we write out the terms of the series we get
If we now write out these terms in reverse order
Adding each pair of terms we then get
First take the sum formula:
Then substitute a = 1, d = 1 to get
So 1+2+3+…+100 = 50 x 101 = 5050 etc
The 5th term of an AP is and the 7th term of the same AP is Find a and d.
Well, writing down the nth terms (n = 5,7) gives
Subtracting gives from which
Substituting this in either equation leads to