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A few sequences…

A few sequences…. 9, 13, 17, 21…. ….. 25, 29. term to term rule: add 4. A few sequences…. 20, 15, 10, 5…. ….. 0, -5. term to term rule: minus 5. A few sequences…. 1, 10, 100, 1000…. ….. 10,000, 100,000. term to term rule: x 10. A few sequences…. 88, 44, 22, 11…. ….. 5.5 , 2.75.

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A few sequences…

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  1. A few sequences… 9, 13, 17, 21…. ….. 25, 29 term to term rule: add 4

  2. A few sequences… 20, 15, 10, 5…. ….. 0, -5 term to term rule: minus 5

  3. A few sequences… 1, 10, 100, 1000…. ….. 10,000, 100,000 term to term rule: x 10

  4. A few sequences… 88, 44, 22, 11…. ….. 5.5, 2.75 term to term rule: half

  5. Sequences the nth term

  6. 1st 2nd 3rd 4th 5th 6th 7th 10, 20, 30, 40, 50, 60, 70…… The position to term rule is: whichever term I’m interested in X 10

  7. 1st 2nd 3rd 4th 5th 6th 7th 4, 8, 12, 16, 20, 24, 28…… The position to term rule is: n whichever term I’m interested in X 4 nth term = n x 4

  8. What is the position to term rule: 2, 4, 6, 8, 10 …. nth term = n x 2 = 2n 6, 12, 18, 24 …. nth term = 6n 5, 10, 15, 20, 25…. nth term = 5n 100, 200, 300, 400…. nth term = 100n What’s the 7th term? 700 What’s the 10th term? 1000 What’s the 18th term? 1,800

  9. more complicated…. 5, 8, 11, 14, 17, 20 ….. +3 +3 +3 +3 +3 common difference is 3 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 + 2 nth term = 3n + 2

  10. To work out the rule for the nth term of a sequence 6, 11, 16, 21, 26… Step 1: Common difference? Step 2: How has the table been shifted? 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 + 1 nth term = 5n + 1

  11. Questions to try: • Work out the rule for the nth term then work out the 100th term • 3, 5, 7, 9, 11, 13…. • 12, 20, 28, 36, 44…. • 19, 29, 39, 49, 59…. • 7, 10, 13, 16, 19…. • 14, 20, 26, 32, 38…. • 55, 60, 65, 70, 75… • 8, 17, 26, 35, 44…. • Extension: • 1, 9, 17, 25, 33…. • -2, 8, 18, 28, 38…. • -2, -4, -6, -8, -10… • 1, 4, 9, 16, 25…. • 3, 6, 11, 18, 27…. !! !!

  12. Real Life Example: • You own a taxi company that charges as follows: • £3.50 for calling the cab • 20p for every minute of journey time Work out a formula for the cost of a journey that’s nminutes long Use your formula to cost a journey of 2 hours

  13. What pattern of matchsticks would follow this sequence rule: 4n + 2

  14. Sequences the nth term

  15. Extension work T(n) = n2 T(n) = 3n2 + n T(n) = 4n2 + n – 1 • For each of these sequences work out the first five terms • What is the first difference? • What is the second difference? • Is there a way of predicting the second difference?

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