WEEK 1 – LESSON 3 SEQUENCES nth TERM

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Presentation transcript:

WEEK 1 – LESSON 3 SEQUENCES nth TERM Angel G. Bassig

STARTER Week 1 – Lesson 3 Starter Please go to our Maths iTunesU course and answer the starter activity for 5 minutes. Week 1 – Lesson 3 Starter

OBJECTIVE To be able to find the nth term of a sequence.

Formulae from Sequences Here are the first five terms of a number sequence . . . 1 2 3 4 5 Position (n) 8 11 14 17 20 Term To get each term in this sequence, we: Multiply the position by 3, then add 5 This means that the formula for this sequence is: 3n + 5 Our aim is to find formulae for different sequences

the final term, we subtract the difference from the first term To find a formula for a number sequence we look at the difference between the terms: Formulae from Sequences 7 11 15 19 23 Difference is the same (4) so the formula starts with 4n + 4 + 4 + 4 + 4 To find the final term, we subtract the difference from the first term Formula 4n + 3 7 - + 4 = 3

the final term, we subtract the difference from the first term To find a formula for a number sequence we look at the difference between the terms: Formulae from Sequences 9 16 23 30 37 Difference is the same (7) so the formula starts with 7n + 7 + 7 + 7 + 7 To find the final term, we subtract the difference from the first term Formula 7n + 2 9 - + 7 = 2

the final term, we subtract the difference from the first term To find a formula for a number sequence we look at the difference between the terms: Formulae from Sequences 2 8 14 20 26 Difference is the same (6) so the formula starts with 6n + 6 + 6 + 6 + 6 To find the final term, we subtract the difference from the first term Formula 6n - 4 2 - + 6 = -4

Answer the following worksheet in pairs Let’s check your understanding … Answer the following worksheet in pairs Time: 10 Minutes

For each of the number sequences below, find a rule for the nth term (tn) and work out the value of t100. Question 1 8, 13, 18, 23, 28, tn= 5n + 3 t100= 5 x 100 + 3 = 503 Question 2 1, 4, 7, 10, 13, tn= 3n - 2 t100= 3 x 100 - 2 = 298 Question 3 2, 9, 16, 23, 30, tn= 7n - 5 t100= 7 x 100 - 5 = 695 9, 15, 21, 27, 33, tn= 6n + 3 t100= 6 x 100 + 3 = 603 Question 4 Question 5 -1, 4, 9, 14, 19, tn= 5n - 6 t100= 5 x 100 - 6 = 494 -3, 1, 5, 9, 13, Question 6 tn= 4n - 7 t100= 4 x 100 - 7 = 393 Question 7 6, 18, 30, 42, 54, tn= 12n - 6 t100= 12 x 100 - 6 = 1194

Answer the following worksheet individually. Let’s check your understanding … Answer the following worksheet individually. Time: 10 Minutes

Formulae from Sequences Find the formula for each of these sequences 1. 2. 3. 4. 5. 6. 7. 8. 7, 12, 17, 22, 27 . . . 7, 11, 15, 19, 23 . . . 2, 9, 16, 23, 30 . . . 13, 22, 31, 40, 49 . . . 12, 32, 52, 72, 92 . . . 11, 13, 15, 17, 19 . . . 1, 12, 23, 34, 45 . . . - 5, 1, 7, 13, 19 . . . 5n + 2 4n + 3 7n - 5 9n + 2 20n - 8 2n + 9 11n + 10 6n - 11

PLENARY Discuss the worksheet answers . Share one or two things learned in today’s lesson.