Year 12 Flipped Learning - Sum of an Arithmetic series

​Year 12 Flipped Learning:

​Lesson 2: Sum of an arithmetic series

​Deadline for Completion:

End of day on Monday 8th May

• Read the information

• Watch the videos

• Complete the notes in your handbook

• Attempt the questions in the quizziz.

​If you need more help please ask a maths teacher during a supported study session.

You need to practice using the online textbook.

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​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

​How to learn a proof:

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

​FINAL EXAMPLE

​a = 7

d = -2

S_N = -2900

n = ?

​ N = 58 or N = -50

Match

Match the following Arithmetic Sequences to their parameters:

• a = 5

  d = -4

• a = 5

  d = 8

• a = -7

  d = 8

• a = -7

  d = 0.5

• a = 2.3

  d = 0.5

5, 1, -3, -7........

5, 13, 21, 29,.....

-7, 1, 9, 17.....

-7, -6.5, -6, -5.5....

2.3, 2.8, 3.3, 3.8, 4.3...

• 5, 1, -3, -7........

• 5, 13, 21, 29,.....

• -7, 1, 9, 17.....

• -7, -6.5, -6, -5.5....

• 2.3, 2.8, 3.3, 3.8, 4.3...

Multiple Choice

Which is the correct formula for the nth term of an arithmetic sequence?

• a + d

• a + bx

• a + (n - 1)d

• a + (n + 1)d

Multiple Choice

What is the correct formula for the sum of an arithmetic series

• $$\frac{n}{2}\left(a\ +\ \left(n\ -\ 1\right)d\right)$$

• $$\frac{n}{2}\left(a\ +\ l\right)$$

• $$\frac{n}{2}\left(a\ +\ \left(n\ +\ 1\right)d\right)$$

• $$\frac{n}{2}\left(2a\ +\ \left(n\ -\ 1\right)d\right)$$

Multiple Choice

The first term of an arithmetic sequence is 14. The fourth term is 32. what is the common difference?

• 6

• 8

• 14

• 4

Multiple Choice

How many term of the Arithmetic Series 5 + 8 + 11 ...

will sum to 670?

• 25

• 20

• 15

• 22

Multiple Choice

How many terms in the Arithmetic Series

64 + 62 + 60 + 58 + ....

will sum to a total of 0?

• -64

• 64

• 46

• 65

Multiple Choice

Find the sum of the first 15 terms of the Arithmetic Series:

2 + 6 + 10 + 14 + .......

• 423

• 465

• 315

• 450

Multiple Choice

Find the sum of the first 40 terms of the Arithmetic Series:

30 + 27 + 24 + 21 + ......

• -1140

• 3540

• -2940

• 1540

Multiple Choice

Find the sum of the Arithmetic Series:

5 + 7 + 9 + ............ + 75

• 4140

• 1040

• 1440

• 1140

Multiple Choice

Find the sum of the Arithmetic Series:

34 + 29 + 24 + ............. + -111

• 1551

• -1515

• -1155

• 1155

Multiple Choice

The sum of the first three terms of an Arithmetic Series is 12

If the 20th term is -32, find the first term and the common difference.

• a = 4

  d = -1.8

• a = 6

  d = 2

• a = 6

  d = -2

• a = 4

  d = -2

Fill in the Blanks

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