1 / 7

Understanding Linear Number Sequences and Patterns

Learn about linear number sequences and patterns, find rules for nth terms, and solve problems involving sequences and diagrams. Explore the relationship between numbers and develop formulas to find any term in a sequence.

bjane
Download Presentation

Understanding Linear Number Sequences and Patterns

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related