3) finding the nth term (2)

9th February 2012

Objective: to be able to find the nth term of an arithmetic sequence. (Grade D)

Skills: Absorption and Making Links

By the end of the lesson:All: work out the rule for a sequence (with n)

Most: will be able to find the nth term of sequence

Some: will be able to write a sequence from the rule in terms of n

Starter

State the rule for the following sequences

1. 16, 26, 36, 46, 56, ...2. 8, 11, 14, 17, 20, ...3. 9, 11, 13, 15, 17, ...4. 0, 4, 8, 12, 16, ...5. -1, 4, 9, 14, 19, ...

From the previous lesson

What were the 2 things we looked for when finding the rule for a sequence?

1. The amount each goes up by

2. What we needed to add or subtract to get

our first term.

nth term

Look at the following sequence

7, 13, 19, 25, 31, ....

What is the rule?x6 + 1

So we can write this as 6n + 1

nth term

Look at the following sequence

3, 7, 11, 15, 19, ....

What is the rule?x4 – 1

So we can write this as 4n – 1

nth term

Look at the following sequence

11, 21, 31, 41, 51, ....

What is the rule?x10 + 1

So we can write this as 10n + 1

How can we find the rule?

Look at the sequence:

4, 7, 10, 13, 16

What is the rule in terms of n

3n + 1

Look at the sequence:

2, 6, 10, 14, 18

What is the rule in terms of n

4n-2

Find the rule in terms of n.....

• Green1. 2, 5, 8, 11, 142. 4, 8, 12, 16, 203. 9, 11, 13, 15, 174. 2, 6, 10, 14, 185. 4, 10, 16, 22, 28

• Red1. 0, 4, 8, 12, 162. 1, 6, 11, 16, 213. 2, 8, 14, 20, 264. 9, 17, 25, 33, 415. -4, 2, 8, 14, 20

Extension3, -2, -7, -12, ...

Answers

• Green1. 3n-12. 4n3. 2n+74. 4n-2 5. 6n-2

• Red1. 4n-42. 5n-43. 6n-4 4. 8n+15. 6n - 10

Extension-5n + 8

What about when the sequence goes down...

What is the nth term of this sequence2, 0, -2, -4, ...

0, -3, -6,-9, ...

Find the rule in terms of n.....

• Green

1) -2, -5, -8, -11, ...2) 4, 1, -2, -5, ...3) 8, 4, 0, -4, -8, ...4) 2, -3, -8, -13, ...5) 10, 6, 2, -2, ....

• Red

1) -3, -7, -11, -15,...2) 1, -3, -7, -11, ...3) 24, 12, 0, -12, ...4) 6, 1, -4, -9, ...5) 4, -3, -10, -17, ...

Answers

• Green1. -3n + 12. -3n + 73. -4n + 124. -5n + 7 5. -4n + 14

• Red1. -4n + 1 2. -4n + 53. -12n + 364. -5n + 11 5. -7n + 11

How does this help us?

• If I know a sequence has a rule 3n how could i find the 100th term?

• If i know a sequence has a rule 5n - 3 how could I find the 100th term?

Questions

• GreenIf I have the sequence

3n find the 1. 1st term2. 4th term3. 10th term4. 100th term

• RedIf I have the sequence

5n – 2 find the 1. 1st term2. 5th term3. 20th term4. 100th term5. 1000th term

To finish

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