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# AS Maths Masterclass - PowerPoint PPT Presentation

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.

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Presentation Transcript

### AS Maths Masterclass

Lesson 1:

Arithmetic series

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.

5 + 7 + 9 + 11 + 13 + … … + 29

– 8 – 5 – 2 + 1 + 4

40 + 30 + 20 + 10 + 0 – 10 – 20 – 30 – 40

“They all have a difference (d) in common!”

E.g. Take 5 + 7 + 9 + 11 + … + 29

Each term is bigger than its previous term by 2

So

Also

In general

Or

“Let’s go straight to the nth term”

We have that

And that

And further that

In general:

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

And so

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