Name: ____________________________________ Date: _________________ Period: ___________ Sorting Sequences Analyze and sort the sequences you have been given into different groups. You may group the sequences in any way you feel is appropriate. However, you must sort the sequences into at least two groups. Part A: Example 1) Record the following information on this page: Sequences • Name that you give to this group • Sequence Letter and the Sequence M) 1, 2, 3, 4, 5, … • Provide a rationale why you created each group J) 1, 11, 111, 111, … T) 2, 4, 6, 8, … We grouped the sequences this way because they are all getting larger. Arithmetic and Geometric Sequences: Sorting Sequences 1 Name: ____________________________________ Date: _________________ Period: ___________ Part B: ______________ Sequences _______________ Sequences A) 5, 8, 11, 14, 17… F) 10, 8, 6, 4, 2 … H) 5, 6 ¼ , 7 ½, 8 ¾, 10 … B) 5, 10, 20, 40, … C) 4, 2, 1, ½, ¼ … I) 1, 10, 100, 1000, 10000 … Analyze the two sets of sequences above. The first set, which includes sequences A, F, and H, are called arithmetic sequences. The second set, which includes sequences B, C, and I, are called geometric sequences. 2) Define the following in your own words: a) Arithmetic Sequence: b) Geometric Sequence: An arithmetic sequence has a common difference, and a geometric sequence has a common ratio. 3) Define the following in your own words. a) Common difference b) Common ratio 4) For each of the following determine if it is an arithmetic or geometric sequence, then identify the common difference or common ratio. !
a) -­‐10, 0, 10, 20, … b) , 1, 3, 9, 27, … !
This sequence is arithmetic
because it has a common
difference of 10. c) 2, 7, 12, 17, … d) 100, 50, 25, 12.5, … e) 0.001, 0.01, 0.1, 1, … f)
g) 52.2, 55.7, 59.2, 62.7, … h) 0.2, 1, 5, 25, … ! ! ! !
, , , , 1, … ! ! ! !
Arithmetic and Geometric Sequences: Sorting Sequences 2 Name: ____________________________________ Date: _________________ Period: ___________ Part C: Arithmetic Sequences Geometric Sequences A) 5, 8, 11, 14, 17… F) 10, 8, 6, 4, 2 … H) 5, 6 ¼ , 7 ½, 8 ¾, 10 … B) 5, 10, 20, 40, … C) 4, 2, 1, ½, ¼, … I) 1, 10, 100, 1000, 10000, … Create a table of values and a graph for each of the sequences above. A) B) F) C) H) I) Arithmetic and Geometric Sequences: Sorting Sequences 3 Teacher Directions Materials: Sequences Cards – 1 set per group/pair pre-­‐cut Objective: By sorting sequences and looking for similarities and differences, students develop definitions for arithmetic and geometric sequences. Teacher Directions: Part A: Students will be grouped in pairs. Pass out handout and sequences. Have a student read the directions and call on students to explain what they are supposed to do. During the sorting, identify interesting groupings that students created. Have these groups come up to share their sort and have the rest of the class try to guess their rule. End the sharing with the arithmetic and geometric grouping. Part B: Tell students that all the sequences in the first group are arithmetic sequences and the sequences in the second group are geometric sequences. Have students define arithmetic and geometric sequences based on the two groupings. Have students share their answer with the class. Students may bring up the idea that in an arithmetic sequence a constant is being added to or subtracted from each term, while in a geometric sequence each term is being multiplied or divided by a given value. Tell students that for the arithmetic sequence this value is called a common difference and for a geometric sequence it is called a common ratio. Have students write their own definitions for common difference and common ratio and selected random students to share their definition with the class. Give pairs a couple of minutes to work on question 4. As you monitor, if it looks like the class understands how to identify each sequence and common difference or ratio, then move on to part C. If it looks like pairs are struggling, have pairs come up and share answers and their reasoning with the class. Part C: Have student’s complete Part C and share answers when finished. Think-­‐Pair-­‐Share “What can you conclude about the graphs of arithmetic and geometric sequences.” Arithmetic and Geometric Sequences: Sorting Sequences 4 Sequence for Sorting A) 5, 8, 11, 14, 17… B) 5, 10, 20, 40, 80… D) 0, 1, 1, 2, 3, 5, 8… C) 4, 2, 1, ½ , ¼ … E) 1, 4, 9, 16, 25 … F) 10, 8, 6, 4, 2 … G) 1, 1, 2, 6, 24, 120 … H) 5, 6 ¼ , 7 ½ , 8 ¾ , 10 … I) 1, 10, 100, 1000, 10000 … Arithmetic and Geometric Sequences: Sorting Sequences 5