Sequences and Patterns – The Rules

Sequences and Patterns – The RulesName:Date:Period:Pattern Rule-Writing Strategy:1. What’s happening to the TERM? Write down any numbers that you thinkmight be helpful.2. How do you get from “n” to “T”? Use the “helpful numbers” from step 1.3. Write your rule – remember the form T = ______4. CHECK that your rule works for lots of term numbers!!!!Exercises:1. Fill in the blanks in the pattern table below.n 1 2 3 4 5 6T 7 14 21 28 35 422. Explain the pattern in #1 in words (use a complete sentence).Students may say something about “going up by 7’s” or “counting by 7’s”3. Write the rule for the pattern in #1: T = 7 n4. Use the rule you came up with in #3 to figure out the 100 th term: 7005. Fill in the blanks in the pattern table below.n 1 2 3 4 5 6T 4 5 6 7 8 96. Explain the pattern in #5 in words (use a complete sentence).Something about going up by ones, but starting at 47. Write the rule for the pattern in #5: T = n + 38. Use the rule you came up with in #7 to figure out the 1000 th term: 1003

9. Sometimes you have to use more than one operation ( + , − , × , ÷ ) when you write arule. Use the rule T = 2n – 1 to fill out the table below.n 1 2 3 4 5 6T 1 3 5 7 9 1110. Now let’s try a more difficult pattern. Look at the table below and decide whichrule fits the pattern. Circle your answer.n 1 2 3 4 5 6 a) T = ½ (n – 1) b) T = ½ (n + 1)T 1 1.5 2 2.5 3 3.5c) T = n – 1 d) T = n + 211. Using the rule you decided on in #10, what would the 75 th term be? 3812. Now that you’ve seen rule with two operations, find the rule for this pattern:n 1 2 3 4 5T 1 4 7 10 13 T = 3 n - 213. Use your rule from #12 to find the 80 th term: 238The graph below shows the rule T = 3 n – 2 as a graph.T3028262422201816141210864200 1 2 3 4 5 6 7 8 9 10 11n