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

Joanna has some sticks that are all the same length.

She arranges them is shapes as shown opposite.

Joanna started with 1029 sticks.

Given that Joanna continues the pattern to make k rows but does not have enough sticks to make the (k + 1)th row,

Find the value of k

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