Different Types of Sequences: IM Alg2.1.3
[url=https://im.kendallhunt.com/HS/teachers/3/1/3/preparation.html]“Different Types of 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
- Alg2.1.3 Lesson
- IM Alg2.1.3 Lesson: Different Types of Sequences
- Alg2.1.3 Practice
- IM Alg2.1.3 Practice: Different Types of Sequences
IM Alg2.1.3 Lesson: Different Types of Sequences
[size=150]Consider the function [math]f[/math] given by [math]f(n)=3n-7[/math]. This function takes an input, multiplies it by 3, then subtracts 7. [br][br][/size]Evaluate [math]f(10)[/math] mentally.
Evaluate [math]f(10)-1[/math] mentally.
Evaluate [math]f(10-1)[/math] mentally.
Evaluate [math]f(5)-f(4)[/math] mentally.
Here are the values of the first 5 terms of 3 sequences:
[*][math]A[/math]: 30, 40, 50, 60, 70, . . .[/*][*][math]B[/math]: 0, 5, 15, 30, 50, . . .[/*][*][math]C[/math]: 1, 2, 4, 8, 16, . . .[/*][br]For each sequence, describe a way to produce a new term from the previous term.[br]
If the patterns you described continue, which sequence has the second greatest value for the 10[sup]th[/sup] term?[br]
Which of these could be geometric sequences? Explain how you know.[br]
Elena says that it’s not possible to have a sequence of numbers that is both arithmetic and geometric.
Do you agree with Elena? Explain your reasoning.
Jada and Mai are trying to decide what type of sequence this could be:
Jada says: “I think this sequence is geometric because in the value column each row is 3 times the previous row.”[br]Mai says: “I don’t think it is geometric. I graphed it and it doesn’t look geometric.”[br][br]Do you agree with Jada or Mai? Explain or show your reasoning.
IM Alg2.1.3 Practice: Different Types of Sequences
Here are the first two terms of an arithmetic sequence:
-2, 4[br]What are the next three terms of this sequence?
11, 111[br]What are the next three terms of this sequence?
5, 7.5[br]What are the next three terms of this sequence?
5, -4[br]What are the next three terms of this sequence?
For each sequence, decide whether it could be arithmetic, geometric, or neither.
200, 40, 8, . . .[br][br]
2, 4, 16, . . .[br][br]Decide whether it could be arithmetic, geometric, or neither.
10, 20, 30, . . .[br]
100, 20, 4, . . .
6, 12, 18, . . .
Complete each arithmetic sequence with its missing terms, then state the rate of change for each sequence.
A sequence starts with the terms 1 and 10.
Find the next two terms if it is arithmetic: 1, 10, ___, ___.
Find the next two terms if it is geometric: 1, 10, ___, ___.[br]
Find two possible next terms if it is neither arithmetic nor geometric: 1, 10, ___, ___.[br][br]
Complete each geometric sequence with the missing terms. Then find the growth factor for each.
The first term of a sequence is 4.
Choose a growth factor and list the next 3 terms of a geometric sequence.[br]
Choose a [i]different[/i] growth factor and list the next 3 terms of a geometric sequence.[br]
Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number.
Starting with the number 0, build a sequence of 5 numbers.[br]
Starting with the number 3, build a sequence of 5 numbers.[br]
Can you choose a starting point so that the first 5 numbers in your sequence are all positive? [br]Explain your reasoning.[br]