Representing More Sequences: IM Alg2.1.7
[url=https://im.kendallhunt.com/HS/teachers/3/1/7/preparation.html]“Representing More Sequences”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.1.7 Lesson
- IM Alg2.1.7 Lesson: Representing More Sequences
- Alg2.1.7 Practice
- IM Alg2.1.7 Practice: Representing More Sequences
IM Alg2.1.7 Lesson: Representing More Sequences
Which one doesn’t belong?
[table][tr][td]A: [math]f(1)=6[/math][br][math]f(n)=f(n-1)-5[/math] for [math]n\ge2[/math][br][br][/td][td]B: [math]f(1)=6[/math][br][math]f(n)=\frac{1}{2}\cdot f(n-1)[/math] for [math]n\ge2[/math][br][br][/td][/tr][tr][td]C: [math]f(0)=6[/math][br][math]f(n)=10\cdot f(n-1)[/math] for [math]n\ge1[/math][/td][td]D: [math]f(1)=6[/math][br][math]f(n)=f(n-1)+n^2[/math] for [math]n\ge2[/math][/td][/tr][/table]
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
[table][tr][td]If your teacher gives you the data card:[/td][td]If your teacher gives you the problem card:[/td][/tr][tr][td][list][*]Silently read the information on your card.[/*][*]Ask your partner “What specific[br] information do you need?” and wait for your partner to ask for information. [br]Only give information that is on your card. (Do not figure out anything for your partner!)[/*][*]Before telling your partner the information, [br]ask “Why do you need to know (that piece of information)?”[/*][*]Read the problem card, and solve the problem independently.[/*][*]Share the data card, and discuss your reasoning.[/*][/list][/td][td][list][*]Silently read your card and think about [/*][*]what information you need to answer [br]the question.[/*][*]Ask your partner for the specific information that you need.[/*][*]Explain to your partner how you are using [br]the information to solve the problem.[/*][*]When you have enough information, [br]share the problem card with your partner, and solve the problem independently.[/*][*]Read the data card, and discuss your reasoning.[/*][/list][/td][/tr][/table]
Make a visual pattern using the point tool in the applet below, starting with Step 0, so the pattern for Step n contains n²+3n+3 dots.
IM Alg2.1.7 Practice: Representing More Sequences
Here is the recursive definition of a sequence:
[size=150][size=100][math]f(1)=10[/math], [math]f(n)=(n-1)-1.5[/math] for [math]n\ge2[/math].[/size][/size][br][br]Is this sequence arithmetic, geometric, or neither?[br]
List at least the first five terms of the sequence.
Graph the value of the term f(n) as a function of the term number n for at least the first five terms of the sequence.
[size=150]An arithmetic sequence [math]k[/math] starts 12, 6, . . .[/size][br][br]Write a recursive definition for this sequence.[br]
Graph at least the first five terms of the sequence.
[size=150]An arithmetic sequence [math]a[/math] begins 11, 7, . . .[/size][br][br]Write a recursive definition for this sequence using function notation. Sketch a graph of the first 5 terms of [math]a[/math] in the graph below.[br]
Explain how to use the recursive definition to find [math]a(100)[/math]. (Don't actually determine the value.)
[size=150]An geometric sequence [math]g[/math] begins 80, 40, . . .[/size][br][br]Write a recursive definition for this sequence using function notation.[br]
Use your definition to make a table of values for g(n) for the first 6 terms.
Explain how to use the recursive definition to find [math]g(100)[/math]. (Don't actually determine the value.)
Match each recursive definition with one of the sequences.
For each sequence, decide whether it could be arithmetic, geometric, or neither. For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?
[math]25,5,1,\ldots[/math]
[math]25,19,13,\ldots[/math]
[math]4,9,16,\ldots[/math]
[math]50,60,70,\ldots[/math]
[math]\frac{1}{2},3,18,\ldots[/math]