Bubble DoublerFunction Machines · functions, their graphs, and sequences

Every bubble splits in two: geometric sequences.

Geometric Sequences

Geometric sequences. In MathBound, the free Algebra I adventure game, Bubble Doubler asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Geometric Sequences. Find the next term or the ratio of a geometric sequence, or say whether a sequence is arithmetic, geometric or neither.

Made by the game’s own question engine. Try each one, then open its steps.

Is

the

sequence

3, 4, 6, 9, \dots

arithmetic,

geometric,

or

neither?

Show the worked steps

$The$ $differences$ $are$ $1, 2, 3,$ $and$ $the$ $ratios$ $are$ $\frac{4}{3}, \frac{3}{2}, \frac{3}{2} .$
$Neither$ $stays$ $the$ $same,$ $so:$ $neither:$ $the$ $differences$ $and$ $the$ $ratios$ $both$ $change .$

Answer: $neither:$ $the$ $differences$ $and$ $the$ $ratios$ $both$ $change$

Which

recursive

rule

describes

the

sequence

4, 12, 36, 108, \dots ?

Show the worked steps

$The$ $first$ $term$ $is$ $4,$ $and$ $each$ $term$ $is$ $3$ $times$ $the$ $one$ $before.$
$So$ $a_{1} = 4, a_{n} = 3 a_{n - 1} .$

Answer: $a_{1} = 4, a_{n} = 3 a_{n - 1}$

The

sequence

3, ?, 27

is

geometric,

with

a

positive

common

ratio.

What

are

the

missing

terms?

Show the worked steps

$From$ $3$ $to$ $27$ $the$ $ratio$ $is$ $applied$ $2$ $times:$ $r^{2} = 9,$ $so$ $r = 3 .$
$So$ $the$ $missing$ $terms$ $are$ $9 .$

Answer: $9$

Textbook	Lessons
Standard course	7.6
Big Ideas Math Algebra 1	6.6, 6.7
Big Ideas Math Algebra 1 (2022)	6.6, 6.7
Carnegie Learning Algebra I	M1 2.1, M1 2.2, M1 2.3, M1 2.4, M3 1.1
CPM Core Connections Algebra	5.1.2, 5.1.3, 5.2.1, 5.2.3, 5.3.2, 5.3.3
CPS Skyline Algebra	1.3, 1.5, 1.7, 1.8, 1.9-1.10, 1.11
enVision Algebra 1	6-4
enVision Algebra 1 (2024)	6-5
Eureka Math Algebra I (EngageNY)	3.3, 5.5
Glencoe Algebra 1	7-7, 7-8
HMH Into Algebra 1	14.1, 14.2
Illustrative Mathematics Algebra 1	5.1-5.2, 5.19-5.20
Illustrative Mathematics Algebra 1 (v.360)	6.1-6.2, 6.19-6.20
MVP Mathematics I (Integrated Math 1)	1.3, 1.5, 1.6, 1.7, 1.9, 1.10
Open Up NC Math 1 (MVP)	1.3, 1.5, 1.6, 1.7, 1.9, 1.10
Pearson Algebra 1 Common Core	7-8
Reveal Algebra 1	9-5, 9-6
SpringBoard Algebra 1	21