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Patterns Comparing
Functions
Geometric Sequences10
0200300400
500
100
300400
500
100200300400
500
100200300400
500
100200300400
500
Arithmetic Sequence
s
Deciphering
Descriptions
200
Final Jeopardy
100 Category 1100 Category 1
Answer
3, 6, 9, ___, ___,___
Answer 100 Category 1Answer 100 Category 1
3, 6, 9, 12, 15, 18
200 Category 1200 Category 1
Answer
The first term of a sequence is 5, and the recursive rule is
an = an -1 – 6
What is the fourth term of the sequence?
Answer 200 Category 1Answer 200 Category 1
5, -1, -7, -13
The fourth term is -13.
300 Category 1300 Category 1
Answer
The first term of a sequence is 7, and the recursive rule is
an = 6an -1
What is the fourth term of the sequence?
Answer 300 Category 1Answer 300 Category 1
7, 42, 252, 1512
The fourth term is 1512.
400 Category 1400 Category 1
Answer
The first term of a sequence is 5, and the recursive rule is
an = 2an -1 + 2
What is the fourth term of the sequence?
Answer 400 Category 1Answer 400 Category 1
5, 12, 26, 545, 12, 26, 54
500 Category 1500 Category 1
Answer
The first term of a sequence is 5, and the recursive rule is
an = 3an -1 – 4
What is the fifth term of the sequence?
Answer 500 Category 1Answer 500 Category 1
5, 11, 29, 83, 2455, 11, 29, 83, 245The fifth term is The fifth term is
245.245.
100 Category 2100 Category 2
Answer
Write the recursive Write the recursive rule if rule if
aa11= 10 d = 3= 10 d = 3
Answer 100 Category 2Answer 100 Category 2Write the recursive Write the recursive
rule if rule if aa11= 10 d = 3= 10 d = 3aann = a = an-1n-1 + 3 + 3
200 Category 2200 Category 2
Answer
Write the Write the explicit/closed rule explicit/closed rule
ififaa11= 15 d = -2= 15 d = -2
Answer 200 Category 2Answer 200 Category 2
Write the rule ifWrite the rule ifaa11= 15 d = -2= 15 d = -2
aann = 15 – 2(n-1) = 15 – 2(n-1)aann = -2n + 17 = -2n + 17
300 Category 2300 Category 2
Answer
Write the first 5 Write the first 5 terms for aterms for ann=6+5n=6+5n
Answer 300 Category 2Answer 300 Category 2
Write the first 5 Write the first 5 terms for aterms for ann=6+5n=6+5n11, 16, 21, 26, 3111, 16, 21, 26, 31
400 Category 2400 Category 2
Answer
Find aFind a2020 for for 10, 6, 2, -2... 10, 6, 2, -2...
Answer 400 Category 2Answer 400 Category 2Find aFind a2020 for for 10, 6, 2, -2… 10, 6, 2, -2…aann =14 - 4n =14 - 4n
so aso a20 = 14 - 4(20) = -6620 = 14 - 4(20) = -66
500 Category 2500 Category 2
Answer
Find the closed and Find the closed and recursive rules for recursive rules for 7, 11, 15, 19, … 7, 11, 15, 19, …
Answer 500 Category 2Answer 500 Category 2
aa11 = 7 d = 4 = 7 d = 4 RecursiveRecursive: a: ann = a = an-1n-1 + 4 + 4
ClosedClosed: : aann = 7 + 4(n – = 7 + 4(n – 1) 1)
100 Category 3100 Category 3
Answer
Which function has a greater Which function has a greater rate of change between rate of change between
[2,4]?[2,4]?Function M Function O 𝒂𝒏 = 𝟏𝟓𝒏+ 𝟑𝟎 Bag Number of Skittles
1 30
2 60
3 90
4 120
Answer 100 Category 3Answer 100 Category 3
Function m: Function m: ROC=slope=25ROC=slope=25
Function oFunction o::(120 – 60)/(4 – 2) =30(120 – 60)/(4 – 2) =30
Function O has a greater rate of change.Function O has a greater rate of change.
200 Category 3200 Category 3
Answer
Which function has a greater Which function has a greater y-intercept?y-intercept?
Function R Function S 𝒂𝒏 = 𝟔𝒏−𝟑 𝒂𝒏 = 𝟑(𝟏𝟒)𝒏
Answer 200 Category 3Answer 200 Category 3
Which function has a greater y-Which function has a greater y-intercept?intercept?
Function R Function S 𝒂𝟎 = 𝟔(𝟎) −𝟑 𝒂𝟎 = −𝟑
𝒂𝟎 = 𝟑(𝟏𝟒)𝟎 𝒂𝟎 = 𝟑
Function S has a greater y-intercept.
300 Category 3300 Category 3
Answer
Which function has a smaller Which function has a smaller y-intercept?y-intercept?
Function H Function K
Month(s) Decaying Grams of Bone Matter
1 100
2 50
3 25
Month(s) Decaying Grams of Bone Matter
2 150
3 50
4 16.7
Answer 300 Category 3Answer 300 Category 3
Which function has a smaller y-Which function has a smaller y-intercept?intercept?Function H Function K
Month(s) Decaying Grams of Bone Matter
1 100
2 50
3 25
Month(s) Decaying Grams of Bone Matter
2 150
3 50
4 16.7
Function H: f(0)=200 Function K: f(0) = 1350
Function H will have a smaller y-intercept.
400 Category 3400 Category 3
Answer
Which function has a greater rate of change
between [1,3]?Function A Function B
Year Portfolio Balance
0 $5
1 $20
2 $80
3 $320
Ava earns 30% interest every year on the money she put into a retirement fund. She originally
invested $300.
Answer 400 Category 3Answer 400 Category 3
Which function has a greater rate of change between [1,3]?Function A Function B
Year Portfolio Balance
0 $5
1 $20
2 $80
3 $320
Ava earns 30% interest every year on the money she put into a retirement fund. She originally
invested $300.
Function A: ROC: (320 – 20)/(3 – 1) = 150
Function B: 𝑓ሺ𝑥ሻ= 300ሺ1+0.3ሻ𝑥
𝑓ሺ1ሻ= 300ሺ1+0.3ሻ1 = 390
𝑓ሺ3ሻ= 300ሺ1+0.3ሻ3 = 659.10
ROC: (659.1 – 390)/(3-1) = 134.55
Function A has a greater rate of change.
500 Category 3500 Category 3
Answer
Function A Function B
Year Portfolio Balance
1 $20
2 $40
3 $80
4 $160
Ava earns 50% interest every year on the money she put into a retirement fund. She originally
invested $20.
Which function has a smaller rate of change
between [2,4]?
Answer 500 Category 3Answer 500 Category 3
Function A Function B
Year Portfolio Balance
1 $20
2 $40
3 $80
4 $160
Ava earns 50% interest every year on the money she put into a retirement fund. She originally
invested $20.
Function A: ROC: (160– 40)/(4 – 2) = 60
Function B: 𝑓ሺ𝑥ሻ= 20ሺ1+0.5ሻ2
𝑓ሺ1ሻ= 20ሺ1+0.5ሻ2 = 45
𝑓ሺ4ሻ= 20ሺ1+0.5ሻ4 = 101.25
ROC: (101.25 –45)/(4-2) = 28.125
Function B has a smaller rate of change.
100 Category 4100 Category 4
Answer
Write the recursive rule if
r = 6 and a1 =7
Answer 100 Category 4Answer 100 Category 4
Write the rule if
r = 6 and a1 =7
an = 6an -1
200 Category 4200 Category 4
Answer
Write the closed rule for
2, 10, 50, 250...
Answer 200 Category 4Answer 200 Category 4
Write the rule for
2, 10, 50, 250…
a1=2 r = 5
an = 2(5)n-1
300 Category 4300 Category 4
Answer
Write the explicit/closed rule for
360,120, 40...
Answer 300 Category 4Answer 300 Category 4
Write the rule for
360,120, 40…
an = 360(1/3)n-1
400 Category 4400 Category 4
Answer
Write out the first 5 terms if
an = 3(2)n-1
Answer 400 Category 4Answer 400 Category 4
Write out the first 5 terms if
an = 3(2)n-1
3, 6, 12, 24, 48
500 Category 4500 Category 4
Answer
Write the explicit and recursive
rules for
6, 18, 54, 162, …
Answer 500 Category 4Answer 500 Category 4a1 = 6 r = 3
Recursive: an = 3an-1
Closed: an = 6(3)n-1
100 Category 5100 Category 5
Answer
You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. Write an equation to model this situation. What is the rate of change?
Answer 100 Category 5Answer 100 Category 5
Y=-400x+40000
ROC: -400
200 Category 5200 Category 5
Answer
You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Write an equation to model this situation. What is the rate of decay?
Answer 200 Category 5Answer 200 Category 5
Y=40000(1-0.065)x
Y=40000(0.935)x
Rate of decay=0.065 or
6.5%
300 Category 5300 Category 5
Answer
You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay $400 each month. How much will you have left to pay on the 12th month?
Answer 300 Category 5Answer 300 Category 5
Y=-400(12)+40000
Y=35200
$35,200
400 Category 5400 Category 5
Answer
You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. If an equation was written to model this situation, what would the y-intercept be?
Answer 400 Category 5Answer 400 Category 5
Y=40000(1-0.065)0
Y=40000
500 Category 5500 Category 5
Answer
You just graduated college and are thinking about how to pay off your loan of $50,000. After paying $10,000 to the bank, you decide to pay 6.5% each month. Your friend also owes $50,000. After paying $10,000 to the bank, your friend decides to pay $500 each month.
Will you or your friend have a smaller average rate of change between [0,3]?
Answer 500 Category 5Answer 500 Category 5
You:f(x)=40000(1-0.065)x
f(0)=40000(1-0.065)0=40000f(3)=40000(1-0.065)3=32696.02
ROC: (32696.02-40000)/(3-0)=-
2434.66
Your Friend:f(x)=-500x + 40000ROC: -500
Double JeopardyDouble JeopardyFill in the blank
for the geometric sequence:
2, ___ , ___ , ___ ,1250
Answer
Double Jeopardy AnswerDouble Jeopardy Answer
2, , , ,1250
10,50,250
Final JeopardyFinal Jeopardy
Write all eight equations I told you to memorize for the test.
Answer
Final JeopardyFinal Jeopardy
