3) finding the_nth_term
- 1. 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
- 3. Starter State the rule for the following sequences 1. 2. 3. 4. 5. 16, 26, 36, 46, 56, ... 8, 11, 14, 17, 20, ... 9, 11, 13, 15, 17, ... 0, 4, 8, 12, 16, ... -1, 4, 9, 14, 19, ...
- 4. 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.
- 5. 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
- 6. 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
- 7. 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
- 8. How can we find the rule? Look at the sequence: Look at the sequence: 4, 7, 10, 13, 16 2, 6, 10, 14, 18 What is the rule in terms of n 3n + 1 What is the rule in terms of n 4n-2
- 9. Find the rule in terms of n..... • Green 1. 2, 5, 8, 11, 14 2. 4, 8, 12, 16, 20 3. 9, 11, 13, 15, 17 4. 2, 6, 10, 14, 18 5. 4, 10, 16, 22, 28 Extension 3, -2, -7, -12, ... • Red 1. 0, 4, 8, 12, 16 2. 1, 6, 11, 16, 21 3. 2, 8, 14, 20, 26 4. 9, 17, 25, 33, 41 5. -4, 2, 8, 14, 20
- 10. Answers • Green 1. 3n-1 2. 4n 3. 2n+7 4. 4n-2 5. 6n-2 Extension -5n + 8 • Red 1. 4n-4 2. 5n-4 3. 6n-4 4. 8n+1 5. 6n - 10
- 11. What about when the sequence goes down... What is the nth term of this sequence 2, 0, -2, -4, ... 0, -3, -6,-9, ...
- 12. Find the rule in terms of n..... • Green • Red 1) 2) 3) 4) 5) 1) 2) 3) 4) 5) -2, -5, -8, -11, ... 4, 1, -2, -5, ... 8, 4, 0, -4, -8, ... 2, -3, -8, -13, ... 10, 6, 2, -2, .... -3, -7, -11, -15,... 1, -3, -7, -11, ... 24, 12, 0, -12, ... 6, 1, -4, -9, ... 4, -3, -10, -17, ...
- 13. Answers • Green 1. -3n + 1 2. -3n + 7 3. -4n + 12 4. -5n + 7 5. -4n + 14 • Red 1. -4n + 1 2. -4n + 5 3. -12n + 36 4. -5n + 11 5. -7n + 11
- 14. 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?
- 15. Questions • Green If I have the sequence 3n find the 1. 1st term 2. 4th term 3. 10th term 4. 100th term • Red If I have the sequence 5n – 2 find the 1. 1st term 2. 5th term 3. 20th term 4. 100th term 5. 1000th term
- 16. To finish • Someone has missed the lesson. You have to send them a text about what you learned in this lesson. Use 160 characters (a text message) to tell them what you learned today