Year 12 Flipped Learning - Sum of an Arithmetic series

​In Lesson 1 you met an Arithmetic Progression:

A sequence of numbers which is defined as having a start number a and a common difference d.

​You should be able to use the formula for the nth term:

U_n = a + (n - 1)d

to calculate terms in a sequence or to solve problems in order to find the value of a or d.

​4, 11, 18, 25, ......

​Try answering this question yourself,

Then watch Martin explain the answer using the QR code or you can access the video in teams in the P11 channel.

​These two formulae are given to you in the formulae booklet.

​You don't need to remember them, but remember that you are given them!

​You will need to learn this "proof" as it is a standard question that is asked frequently in exam papers!

​It follows Gauss' solution for pairing numbers...

​Have a try yourself - then watch the following video for how it should be done in an exam

1. Read the proof or watch the video

2. Cover the example or stop the video

3. Without cheating! have a go at writing the proof yourself.

4. Check your written proof against the example or the video.

​The more times you practise this... the better you will remember it!

​Use the formula.

This questions is just "fancy substitution"!

​a = -4

d = 9

n = 35

​Check your answer: 5215

​Use the formula.

This question is just "solving an inequality"!

​a = 4

d = 5

n = ?

S_n > 2000

​Remember to use a sketch graph and your calculator to help you solve your quadratic inequality!

​ n > 27.99 or n < -28.59

n is a term in a sequence and is not negative, nor a decimal.

So what is n?

​a + 8d = 18

​nth term formula: U_n = a + (n - 1)d

​9a + 36d = 72

​Remember to use your calculator to help you solve your simultaneous equations!

​a = -2 and d = 2.5

​a = 7

d = -2

S_N = -2900

n = ?

​ N = 58 or N = -50