Recommended
Recommended
More Related Content
Similar to formula.pptx
Similar to formula.pptx (20)
Recently uploaded
Recently uploaded (20)
formula.pptx
- 1. Sequences Starter: 09/06/2023 Draw the next picture in this pattern.
- 2. Sequences Starter: 09/06/2023 What is the first term of the sequence? 8, 11, 14, 17,β‘,β‘
- 3. Sequences Definitions: 09/06/2023 Sequence A sequence is a list of numbers in a special order. Term Each number in a sequence is called a term. Term to Term Rule Defines the value of each term in a sequence Linear Sequence A sequence that increases/decreases by the same amount each time.
- 4. Sequences 1 Discussion 1: Sam is a biologist for a seed. She records the growth of Brand X bean plants over six days. Sam notices that Brand X bean plants grow to a number pattern. She decides to create a table to show this. 09/06/2023 Day 1 Day 2 Day 3 Day 4 Day 5
- 5. plants over six days. Sam notices that Brand X bean plants grow to a number pattern. She decides to create a table to show this. The number pattern can be written as a sequence. Day 1 Day 2 Day 3 Day 4 Day 5 Day 1 2 3 4 5 Number of leaves 2 4 6 8 10
- 6. Sequences 1 Discussion 2: Look at this Spanish tile pattern and determine the sequence that was used and find the next five terms. The sequence for the pattern is 1, 5, 9, 13β¦ The term-to-term rule: The next five terms are 09/06/2023 1 tile 5 tiles 9 tiles 13 tiles 17 21 25 29 33 Starts at 1 and add 4
- 7. Sequences 1 Discussion 3: a) Write a sequence for the number of dots in each term as the sequence progresses, b) What is the term-to-term rule for the sequence? c) Use the rule to extend the sequence to the 5th term 09/06/2023 1, 3, 5, ........ Starts at 1, and add 2 1 3 5 7 9
- 8. Sequences Examples: 09/06/2023 eg1 Find the T2T rule and the next two terms of the sequence. 3, 5, 7, 9 β¦ eg2 Find the T2T rule and the next two terms of the sequence. 2, 8, 32, 128 β¦ Try Find the T2T rule and the next two terms of the sequence. 25, 28, 31, 34 β¦ Try Find the T2T rule and the next two terms of the sequence. 2, 6, 18, 54 β¦ T2T Rule: +2 Next 2 terms: 11, 13 β¦ T2T Rule: +3 Next 2 terms: 37, 40 β¦ T2T Rule: Γ 4 Next 2 terms: 512, 2048 β¦ T2T Rule: +3 Next 2 terms: 162, 486 β¦
- 9. Task 1: 1 Find the term to term rule and the next two terms in the sequence. a 4, 6, 8, 10 β¦ b 5, 7, 9, 11 β¦ c 2, 9, 1, 1, 7 β¦ There are non examples d 2, 4, 8, 16 β¦ e 7, 10, 13, 16 β¦ f 21, 19, 17, 15 β¦ g 1024, 256, 64, 16 β¦ h 0, 6, 12, 18 β¦ i β9, β3, 3, 9 β¦ j 1, 4, 9, 16, 25 β¦ k β3, 3, 13, 27 β¦ l 0, 6, 16, 30 β¦ m 2π₯, 4π₯, 6π₯, 8π₯ β¦ n 2π₯, 4π₯, 8π₯, 16π₯ β¦ o 2π₯ + 2, 3π₯ + 5, 4π₯ + 8 +π 12, 14 β¦ +π 13, 15 β¦ π΅ππ β π¬ππππππ Γ π 32, 64 β¦ +π 19, 22 β¦ βπ 13, 11 β¦ Γ· π 4, 1 β¦ +π 24, 30 β¦ +π 15, 21 β¦ +π, +π, +π β¦ 36, 49 β¦ +π, +ππ, +ππ β¦ 45, 67 β¦ +π, +ππ, +ππ β¦ 48, 70 β¦ +ππ 10π₯, 12π₯ β¦ Γ π 32π₯, 64π₯ β¦ +(π + π) 5π₯ + 11, 6π₯ + 14 β¦ 2 Find the term to term rule and the draw the next picture. +3 π ππ’ππππ 3 Is 318 a term in the sequence 1, 9, 17, 25β¦? No the terms are all odd numbers.
- 10. Sequences Examples: 09/06/2023 eg3 Use the T2T rule to find the first 5 terms in the sequence. Starts at 6, +π Try Use the T2T rule to find the first 5 terms in the sequence. Starts at 6, βπ 6 9 12 15 18 6 3 0 -3 -6
- 11. Task 2: 1 Use the T2T rule to find the first 5 terms in the sequence. a ππ‘πππ‘: π π π’ππ: +π b ππ‘πππ‘: π π π’ππ: +π c ππ‘πππ‘: π π π’ππ: +π 4, 7, 10, 13, 16 5, 8, 11, 14, 17 5, 9, 13, 17, 21 d ππ‘πππ‘: π π π’ππ: Γ π e ππ‘πππ‘: π π π’ππ: βπ f ππ‘πππ‘: ππ π π’ππ: βπ 1, 3, 9, 27, 81 5, 1, β3, β7, β11 10, 5, 0, β5, β10 g ππ‘πππ‘: π π π’ππ: Γ π πππ + π 1, 3, 7, 15, 31, 63 h ππ‘πππ‘: ππ π π’ππ: +π πππ Γ· π 33, 17, 9, 5, 3 i ππ‘πππ‘: π + π π π’ππ: +(ππ + π) π₯ + 5, 3π₯ + 8, 5π₯ + 11, 7π₯ + 14, 9π₯ + 17 j ππ‘πππ‘: ππ π π’ππ: Γ (ππ) 2π₯, 4π₯2 , 8π₯3 , 16π₯4 , 32π₯5 2 The rule is to add four. Explain why she has not described the rule for a sequence. The first term of her sequence is a factor of 18. Come up with 3 different sequences. Sofia is writing a sequence. a b
- 12. Sequences To Finish: 09/06/2023 Find the term to term rule for the sequence. 5, 8, 11, 14 β¦
- 13. Sequences To Finish: 09/06/2023 Find the next two terms of the sequence. 5, 8, 11, 14, ο―, ο― β¦
- 14. Sequences To Finish: 09/06/2023 Is this a linear sequence? 5, 8, 11, 14 β¦
- 15. Sequences To Finish: 09/06/2023 Is 2043 a term in this sequence? 7, 12, 17, 22 β¦
- 16. Sequences 2 Discussion: 09/06/2023 Take a look at the sequence 7, 11, 15, 19 β¦ Find the term to term rule. +4 Find the next two terms. 23 27 Find the 10th term. 31 35 39 43 Find the 80th term. It will take a long time to find this term using the term to term rule. We can use the position to term rule. 4π + 3 = 4 80 + 3 = 320 + 3 = 323
- 17. Sequences 2 Definitions: 09/06/2023 Position to Term Rule a rule that defines the value of each term in a sequence with regard to its position. nth Term Rule Also known as the position to term rule. Uses algebra to work out the term given the position. π The position of the nth term. Position 1 2 3 4 β¦ π Sequence 7 11 15 19 β¦ ππ + π nth term rule
- 18. Sequences Examples: 09/06/2023 eg1 Use the nth term rule to find the first four terms. ππ eg2 Use the nth term rule to find the first four terms. ππ + π Try Use the nth term rule to find the first four terms. ππ Try Use the nth term rule to find the first four terms. ππ β π π 1 2 3 4 2π 2 4 6 8 π 1 2 3 4 5π 5 10 15 20 π 1 2 3 4 2π + 4 6 8 10 14 π 1 2 3 4 5π β 3 2 7 12 17
- 19. Task 2: 1 Find the first 4 terms of each sequence. a 3π b 4π c 4π + 1 d 4π + 7 e 4π β 10 f π β 10 3, 6, 9, 12 4, 8, 12, 16 5, 9, 13, 17 11, 15, 19, 23 β6, β2, 2, 6 β9, β8, β7, β6 g π + 10 h 1 2 π + 10 i 1 2 π β 2 11, 12, 13, 14 10.5, 11, 11.5, 12 β1.5, β1, β0.5, 0 2 Match the rule to the sequence. 9, 12, 15, 18 7, 8, 9, 10 6, 12, 18, 24 9, 15, 21, 27 6π π + 6 6π + 3 3π + 6 3 Find the first 4 terms of each sequence. a β2π b 3 β 2π c 3 β 4π β2, β4, β6, β8 1, β1, β3, β5 β1, β5, β9, β13 d π2 e π3 f 3π 1, 4, 9, 16 1, 8, 27, 64 3, 9, 27, 81
- 20. Sequences 2 To Finish: 09/06/2023 Write the first 4 terms of the sequence 5π β 2
- 21. Sequences 2 To Finish: 09/06/2023 What is the 10th term of the sequence. 5π β 2
- 22. Sequences 2 To Finish: 09/06/2023 What is the 21st term of the sequence. 2π + 6
- 23. Sequences 3 Starter: 09/06/2023 Sequences Which sequences below are linear? 1) 2, 5, 8, 11 β¦ 2) 24, 19, 14, 9 β¦ 3) 3, 6, 12, 24 β¦ 4) 120π₯, 60π₯, 30π₯, 15π₯ β¦ Write the term to term rule each sequence. 1) 4, 14, 24, 34 β¦ 2) 1, 4, 16, 64 β¦ Use the position to term rule to write the first four terms of the sequence. ππ β π Use the nth term rule to find the 8th term of the sequence. ππ β ππ
- 24. Sequences 3 Starter: 09/06/2023 Sequences Which sequences below are linear? 1) 2, 5, 8, 11 β¦ Yes 2) 24, 19, 14, 9 β¦ Yes 3) 3, 6, 12, 24 β¦ No 4) 120π₯, 60π₯, 30π₯, 15π₯ β¦ No Write the term to term rule each sequence. 1) 4, 14, 24, 36 β¦ + 10 2) 1, 4, 16, 64 β¦ Γ 4 Use the position to term rule to write the first four terms of the sequence. ππ β π Use the nth term rule to find the 8th term of the sequence. ππ β ππ 3, 8, 13, 18 β¦ 20
- 25. Sequences 3 Discussion: 09/06/2023 What is the nth term rule for this sequence? 6 12 18 24 β¦ +6 +6 +6 +6 Position (π) 1 2 3 4 β¦ π Sequence 6 12 18 24 β¦ 6π What is the nth term rule for this sequence? 4 10 16 22 β¦ +6 +6 +6 +6 Position (π) 1 2 3 4 β¦ π Sequence 4 10 16 20 β¦ 6π β 2
- 26. Sequences 3 Discussion: 09/06/2023 What is the nth term rule for this sequence? 9 15 21 27 β¦ +6 +6 +6 +6 Position (π) 1 2 3 4 β¦ π Sequence 9 15 21 27 β¦ 6π + 3
- 27. Sequences 3 Examples: 09/06/2023 eg1 Find the nth term rule for π, π, ππ, ππ β¦ eg2 Find the nth term rule for π, π, π, π β¦ Try Find the nth term rule for π, π, π, ππ β¦ Try Find the nth term rule for π, π, βπ, βπ β¦ 5 8 11 14 2 5 8 11 8 6 4 2 6 2 -2 -6 +3 +3 +3 ππ 3 6 9 12 +2 ππ + π +3 +3 +3 ππ 3 6 9 12 -1 ππ β π -2 -2 -2 βππ β2 β4 β6 β8 +10 βππ + ππ -4 -4 -4 βππ β4 β8 β12 β16 +10 βππ + ππ
- 28. Find the nth term rule for the following sequences. a 3, 5, 7, 9 ... b 4, 6, 8, 10 ... c 2, 4, 6, 8 β¦ d 5, 10, 15, 20 β¦ e 2, 7, 12, 17 β¦ f 7, 12, 17, 22 β¦ g -2, 3, 8, 13 β¦ h -4, 6, 16, 26 β¦ i -40, 60, 160, 260 β¦ j 2, -1, -4, -7 β¦ k 2, -2, -6, -10 β¦ l 4, -4, -12, -20 β¦ 2 Match the sequences to the nth term rule. 1 5, 7, 9, 11 β¦ 5, 8, 11, 14 β¦ 4, 5, 6, 7 β¦ 3π + 2 2π + 3 π + 3 Find the nth term rule of the sequence. 3 Is Jasper correct for the sequence 10, 14, 18, 22β¦? Explain 5 The nth term rule is π + 4 Find the nth term rule for 1 2 , 2 5 , 3 8 , 4 11 β¦ 6 2π + 1 2π + 2 2π 5π 5π β 3 5π + 2 5π β 7 10π β 14 100π β 140 β3π + 5 β4π + 6 β8π + 12 3π β 1 A sequence has a T2T rule of +6. The 9th term is 57. Find the nth term rule. 4 6π + 3 4π + 6 π 3π β 1
- 31. Practice 4, page 428 β’ Questions 1, 2, 3 Mixed Practice, page 430 β’ Questions 3, 5, 6, 7