"Uh-rith-muh-tic"
Sequences
Sequences
It's not geometry, it's geometric!
The Krabby Patty
Secret Formula
Secret Formula
"This Ain't Square Dancin', This is Line Dancin'!"
My Fiance Couldn't Think of a Name for This
100
Given the sequence, find the common difference. (notation matters)
7, 10, 13, 16, 19,...
d = 3
100
Given the sequence:
-2, 6, -18, 54, -162,...
Tell whether the sequence is geometric or not and explain how you know.
Yes, it's geometric because it has a common ratio of -3.
100
Slope-Intercept Form
y=mx+b
100
Find the slope of the line given the graph
m = (rise)/(run) = (-3)/1 = -3
100
Given the following word problem...
"De'Marc is in study hall reading The Hunger Games. After 20 minutes, he is on page 151. After 45 minutes, he is on page 181. How many pages had De'Marc read prior to study hall?"
Identify which formula you would use to solve the problem.
A) Standard Form
B) Point-Slope (Given two points)
C) Slope-Intercept
D) Point-Slope (Given slope and a point)
B) Point-Slope (Given two points)
200
Faith is trying to save money for a car. She started with $300 in her savings account and plans to save a hundred more every month.
Give the recursive formula for the nth month.
a_1 = 300
a_n = a_(n-1) + 100
200
You notice that a geometric sequence is dividing by 9 each time.
Write the common ratio so that it states what it would be in terms of multiplication.
r=1/9
200
Standard Form
Ax+By=C
200
Calculate the x- and y-intercepts of the equation.
6x - 2y = -18
x-intercept: -18/6 = -3
y-intercept: (-18)/-2 = 9
200
Given the following word problem:
"The start-up cost to join eTunes music is $7.95 plus $0.95 per song downloaded. If Andrew spent $26, write and solve a linear equation to find how many songs he downloaded."
Identify the slope/rate of change AND the starting point.
Slope = $0.95 per song downloaded
Starting Point = $7.95 start-up cost to join
300
The explicit formula for an arithmetic sequences can be written two different ways.
Give BOTH ways of writing it.
a_n = a_1 + d(n-1)
OR
a_n = a_0 +dn
300
In its first year open, Lamiya's company made $680,000 in profits. With the ability to expand, she predicts the company profits will continue increasing by 12% each year until she ultimately rules the planet.
Give the common ratio.
r = 1 + 0.12 = 1.12
300
Point-Slope Form
y-y_1=m(x-x_1)
300
Give the slope-intercept form equation of the line
y=x-2
300
Given the following word problem:
"Karyss is selling wreaths and poinsettias for her chorus fundraiser. Wreaths cost $27 each and poinsettias cost $20 each. If she sold 15 poinsettias and made $543, how many wreaths did she sell?"
Label the variables (w/ numbers):
A =
B =
C =
A = 27
B = 20
C = 543
400
In the last year, Bralen has decided to take up tennis as a hobby. He just started buying his own tennis balls instead of borrowing a friend's. He started with only three to his name but will be adding 5 more each month.
Write an explicit rule for how many tennis balls Bralen will have in the nth month.
a_n = 3 + 5(n-1)
OR
a_n = -2 + 5n
400
The explicit rule is written incorrectly in step 1. It either has to be a_n = a_1r^(n-1) OR a_n = a_0r^n .
a_n = a_1r^(n-1)
48 = a_1(6)^(2-1)
48 = a_1(6)^(1)
8 = a_1
a_n = 8(6)^(n-1)
400
Slope Formula
m = (y_2-y_1)/(x_2-x_1)
400
Calculate the slope of the line that passes through the two points:
(5, -4) and (-3, -2)
m = (-2 - -4)/(-3-5) = 2/-8 = -1/4
400
Given the following word problem:
"The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Write and solve an equation to find the cost of 4 lessons."
Calculate the slope/rate of change and write the point-slope form of the equation.
m = (122-82)/(11-7) = 40/4 = 10
Rate of Change = $10/lesson
500
Faith is trying to save money for a car. She started with $300 in her savings account and plans to save a hundred more every month.
Use an explicit formula to calculate how much money she will have saved by the 17th month.
a_17 = 300 + 100(17-1)
a_17 = 300 + 100(16)
a_17 = 300 + 1600
a_17 = $1900
OR
a_17 = 200 + 100(17)
a_17 = 200 + 1700
a_17 = $1900
500
In its first year open, Lamiya's company made $680,000 in profits. With the ability to expand, she predicts the company profits will continue increasing by 12% each year until she ultimately rules the planet.
Use an explicit rule to calculate Lamiya's company profits after its 6th year.
a_6 = 680,000(1.12)^(6-1)
a_6 = 680,000(1.12)^5
a_6 = $1,198,392.34
500
Sum Formula
S_n=(n(a_1+a_n))/2
500
Convert the equation into slope-intercept form.
y+5=-4(x-2)
y+5=-4(x-2)
y+5=-4x+8
y=-4x+3
500
Solve the word problem:
"Touchdowns are worth 7 points and field goals are worth 3 points. The Raiders scored 44 points against Ravens and managed 5 touchdowns. Write and solve a linear equation to find how many field goals the Raiders made."
A = 7 B = 3 C = 44
x-value = # touchdowns y-value = # field goals
Equation: 7x + 3y = 44
7(5) + 3y = 44
35 + 3y = 44
3y = 9
y = 3
3 field goals