Domino TopplerFunction Machines · functions, their graphs, and sequences

Each domino knocks over the next: recursive rules.

Recursive Rules

Recursive rules. In MathBound, the free Algebra I adventure game, Domino Toppler asks these problems, and the only way past is to solve them.

Part of Functions: chapter 4 of the standard course.

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

What you will practice

Recursive Rules. Find terms from a recursive rule that adds, or that multiplies and adds, including a spreadsheet formula filled down.

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

In

a

spreadsheet,

cell

A 1

holds

3 .

Cell

A 2

holds

the

formula

= A 1 + 8,

and

it

is

filled

down

column

A,

so

each

cell

uses

the

cell

above

it.

What

number

shows

in

cell

A 8 ?

Show the worked steps

$Each$ $cell$ $is$ $the$ $cell$ $above,$ $plus$ $8 .$
$Down$ $the$ $column:$ $3, 11, 19, 27, 35, 43, 51, 59 .$ $Cell$ $A 8$ $shows$ $59 .$

Answer: $59$

List

the

first

four

terms

of

the

sequence

a_{1} = - 8, a_{n} = a_{n - 1} - 5 .

Show the worked steps

$Start$ $at$ $a_{1} = - 8;$ $each$ $term$ $after$ $it$ $is$ $the$ $last$ $one$ $- 5 .$
$So$ $the$ $terms$ $are$ $- 8, - 13, - 18, - 23 .$

Answer: $- 8, - 13, - 18, - 23$

A

sequence

has

a_{n} = 2 a_{n - 1}

and

a_{4} = 48 .

Find

a_{1} .

Show the worked steps

Answer: $6$

Textbook	Lessons
Standard course	4.6, 7.6
Big Ideas Math Algebra 1	6.7
Big Ideas Math Algebra 1 (2022)	6.7
Carnegie Learning Algebra I	M1 2.3, M1 2.4
CPM Core Connections Algebra	5.2.3, 5.3.3
CPS Skyline Algebra	1.2, 1.3, 1.4, 1.5, 1.8, 1.11
enVision Algebra 1	3-4, 6-4
enVision Algebra 1 (2024)	3-4, 6-5
Eureka Math Algebra I (EngageNY)	1.25-1.28, 3.1-3.2, 5.5
Glencoe Algebra 1	7-8
HMH Into Algebra 1	7.1, 14.1, 14.2
Illustrative Mathematics Algebra 1	1.6-1.8
Illustrative Mathematics Algebra 1 (v.360)	1.6-1.8
MVP Mathematics I (Integrated Math 1)	1.2, 1.4, 1.5, 1.7, 1.10
Open Up NC Math 1 (MVP)	1.2, 1.4, 1.5, 1.7, 1.10
Pearson Algebra 1 Common Core	4-7, 7-8
Reveal Algebra 1	9-6
SpringBoard Algebra 1	11, 21