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Linear Number Sequences/Patterns

+ 2. ?. 5. 8. 11. 14. 17. Linear Number Sequences/Patterns. A linear number sequence is a sequence of numbers that has a constant difference between adjacent terms. Consider the first five terms of the number sequence shown:.

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Linear Number Sequences/Patterns

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  1. + 2 ? 5 8 11 14 17 Linear Number Sequences/Patterns A linear number sequence is a sequence of numbers that has a constant difference between adjacent terms. Consider the first five terms of the number sequence shown: 1st 2nd 3rd 4th 5th................................nth 5, 8, 11, 14, 17,………………..? We want to obtain a general rule that gives us the value of any term (nth) in the sequence as a function of the term’s position. 3n + 2 Can you see how the numbers of this sequence are related to those in the 3 times table? Adjacent numbers in the 3 times table also differ by 3. The terms in this sequence are 2 bigger than the numbers in the 3 times table. nth= 3n + 2

  2. 1st 2nd 3rd 4th 5th.........nth 5, 8, 11, 14, 17,…..? 3 3 3 3 + 2 - 1 ? 3 7 11 15 19 nth= 3n + 2 3, 7, 11, 15, 19,…..? nth= 4n - 1 4 4 4 4 4n - 1

  3. 1st 2nd 3rd 4th 5th.........nth nth= 3n + 2 5, 8, 11, 14, 17,…..? 3 3 3 3 3, 7, 11, 15, 19,…..? nth= 4n - 1 4 4 4 4 - 1 + 3 + 2 ? 8 13 18 23 28 8, 13, 18, 23, 28,…..? nth= 5n + 3 5 5 5 5 5n + 3

  4. Difference 7  7n 7  2  - 5 Difference 6  6n 6  9  + 3 Example Question 2 For the number sequence below: (a) Find the nth term (b) Use your rule to find the 75th term 9, 15, 21, 27, 33,…… Example Question 1 For the number sequence below: (a) Find the nth term (b) Use your rule to find the 58th term 2, 9, 16, 23, 30,…… (a) nth= 7n - 5 (b) t58= 7 x 58 - 5 = 401 (a) tn= 6n + 3 (b) t75= 6 x 75 + 3 = 453

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

  6. Number sequences can be used to solve problems involving patterns in diagrams. 4 3 2 1 1 3 5 7 How many wooden braces (B) will there be, in the 20th panel (P)? 1 3 2 7 10 4 How many squares of chocolate (S) will the 10th diagram (D) contain? S = 2D - 1 S10 = 2 x 10 - 1 = 19 B = 3P + 1 B20 = 3 x 20 +1= 61

  7. 3 How many stone slabs (S) will the 15th diagram (D) contain? 2 1 1 5 9 How many steel braces (B) will there be, in the 28th panel (P)? 1 2 3 6 11 16 S = 4D - 3 S15 = 4 x 15 – 3 = 57 B = 5P + 1 B28 = 5 x 28 + 1 = 141

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