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Linear Sequences

Linear Sequences. Slideshow 7, Room 307 Mr Richard Sasaki, Mathematics. Objectives. Vocabulary Check 4 Find sequence patterns Make formulae for each number in a sequence. Vocabulary Check 4. Good luck, in this vocabulary check there are many decoys! You have six minutes, try your best!.

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Linear Sequences

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  1. Linear Sequences Slideshow 7, Room 307 MrRichard Sasaki, Mathematics

  2. Objectives • Vocabulary Check 4 • Find sequence patterns • Make formulae for each number in a sequence

  3. Vocabulary Check 4 Good luck, in this vocabulary check there are many decoys! You have six minutes, try your best!

  4. Answers 5 5 3 240 Yen 15 5 1050ml 7 5 (naan bread and tandoori chicken) 4

  5. Answers • And here is your rating… • 1 Terrible… • 2 Disaster… • 3 Poor… • 4 So-so… • 5 Okay • 6 Good • 7 Great! • 8 Fantastic!! • 9 Super Excellent!! • 10 Unbelievable!!!!

  6. Sequences A sequence is an ordered number pattern. It is often easy to see which numbers are missing in the pattern or the next numbers that come. 3, 5, 7, 9, __, 13, __, __ 11 15 17 Here it was easy to tell that the numbers go up 2 every step to the right. (If numbers go up the same amount every step then the sequence is linear.)

  7. Sequences With sequences, it is important to understand each number’s placement. 1 2 3 4 5 6 7 8 9 10 (n) 20 3, 5, 7, 9, __, 13, __, __ 11 15 17 37 We call the position n. So for the second position (where n = 2), we have 5. How about the 20th position (n = 20)? Just randomly thinking about it in our heads isn’t a good way of doing this. Can we make a formula?

  8. Sequences The formula must be “in terms of” n. “In terms of” means that the unknown, the letter is n. 1 2 3 4 5 6 7 8 9 10 (n) 20 3, 5, 7, 9, __, 13, __, __ 11 15 17 37 Let’s try to make a formula for this sequence. (2n means 2 x n.) 2 n Is that it? Let’s check. The formula must contain the unknown n as we relate it to each number’s position. The formula goes up in twos. So we need to multiply the unknown by 2.

  9. Sequences 1 2 3 4 5 6 7 8 9 10 (n) 20 Position Sequence 3, 5, 7, 9, __, 13, __, __ 11 15 17 37 6, 2, 4, 8, 10, 12, 14, 16 Test All of the numbers in our test are slightly off, how much by? Yes, we need to add 1 to each. 2 n + 1 That’s about it! Let’s try another.

  10. Sequences Example Find a formula in terms of n for the sequence below. 7, 10, 13, 16, 19, … Well it’s going up in 3s so we must have… 3 n What’s the other bit? There is an easier way to think about this…

  11. Sequences Example A trick is to find the 0th term. What is the 0th term? 0 1 2 3 4 5 (n) __, 4 7, 10, 13, 16, 19, … We then add this onto the formula to perfect it. 4 3 n + n = 2 n = 3 n = 1 Let’s try it out. It seems fine. 7, 10, 13,

  12. Sequences Now try the worksheets! Example Find a formula for the nthterm for the sequence below. Also, find out what the 50th term is. 2, 7, 12, 17, 22, … -3, 5 How much do the numbers increase by? -3 What would the 0th term be? What is the formula for the nthterm? 3 5 n - 5n – 3, n = 50 What would the 50th term be? (5 x 50) - 3 247

  13. Answers – Easy & Medium 8 3 12 14 21 39 33 2 3n + 2 3 1 -3 4 19 -5 50 62 66 2 -10 -14 2n + 1 0.5n + 1 5n -3n - 4 2 0.5 8n - 5 n – 5 -3 22 28 10 40 8 6n - 2 6 x 10 – 2 = 58 1 1 6 x 100 – 2 = 598 0 -4 -5 -2 9 7 13 11 5 2n + 2 2 x 50 + 3 = 103

  14. Answers - Hard 6 __, __, __, 14, 17, … n + 3 -n + 2 -1 -2 (2,) 5, 8, 11, 14, 17, … 3n + 2 12 6 16 2n + 8 -5 11n - 16 6 7 4 9 3n - 3 1 -3n + 13 4.5 5.5 n + 2.5 2an 6a 2n n + 1 1 5 9 13 17 21 25 29 3n + 1 (added together) 4 x 35 – 3 = 137

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