Patterns Arithmetic Series

Geometric Sequences10

0200300400

500

100

300400

500

100200300400

500

100200300400

500

100200300400

500

Arithmetic Sequence

s

Geometric Series

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

20, 12, 4 , ___, ___,___

Answer 200 Category 1Answer 200 Category 1

20, 12, 4 , -4, -12, -20

300 Category 1300 Category 1

Answer

800, 400, 200, , 800, 400, 200, , ___, ___,______, ___,___

Answer 300 Category 1Answer 300 Category 1

800, 400, 200, 100, 800, 400, 200, 100, 50,2550,25

400 Category 1400 Category 1

Answer

3, 5, 8, 12, ___, 3, 5, 8, 12, ___, ___,______,___

Answer 400 Category 1Answer 400 Category 1

3, 5, 8, 12, 17, 3, 5, 8, 12, 17, 23,3023,30

500 Category 1500 Category 1

Answer

1,1,2,3,5,8 , ___, 1,1,2,3,5,8 , ___, ___,______,___

Answer 500 Category 1Answer 500 Category 1

1,1,2,3,5,8 , 13, 1,1,2,3,5,8 , 13, 21,3421,34

100 Category 2100 Category 2

Answer

Write the rule if Write the rule if aa11= 10 d = 3= 10 d = 3

Answer 100 Category 2Answer 100 Category 2

Write the rule if Write the rule if aa11= 10 d = 3= 10 d = 3aann = 7 + 3n = 7 + 3n

200 Category 2200 Category 2

Answer

Write the rule ifWrite the rule ifaa33= 15 d = -2= 15 d = -2

Answer 200 Category 2Answer 200 Category 2

Write the rule ifWrite the rule ifaa33= 15 d = -2= 15 d = -2aann = 21 - 2n = 21 - 2n

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 rule if aFind the rule if a33 = = 5 and a5 and a77 = 9 = 9

Remember this is an Remember this is an arithmetic categoryarithmetic category

Answer 500 Category 2Answer 500 Category 2

Find the rule if aFind the rule if a33 = 5 = 5 and aand a77 = 9 = 9

__,__,5,__,__,__,9__,__,5,__,__,__,9d = (9-5)/(7-3) =1d = (9-5)/(7-3) =1

aann = 2 +1n = 2 +1n

100 Category 3100 Category 3

Answer

Find the SFind the S33 for for 10, 8, 6...10, 8, 6...

Answer 100 Category 3Answer 100 Category 3

Find the SFind the S33 for for 10, 8, 6…10, 8, 6…

10+8+6 =2410+8+6 =24

200 Category 3200 Category 3

Answer

Find the SFind the S55 for for 3,7,11,15...3,7,11,15...

Answer 200 Category 3Answer 200 Category 3Find the SFind the S55 for for 3,7,11,15…3,7,11,15…

3+7+11+15+19=53+7+11+15+19=555

or 5/2(3+19)=55or 5/2(3+19)=55

300 Category 3300 Category 3

Answer

Find the SFind the S77 if aif ann = 2 - 3n = 2 - 3n

Answer 300 Category 3Answer 300 Category 3

Find the SFind the S77 if aif ann = 2 - 3n = 2 - 3n

-1+ -4+-7+-10+--1+ -4+-7+-10+-13+--16+-19= -7013+--16+-19= -70

400 Category 3400 Category 3

Answer

i = 112

Answer 400 Category 3Answer 400 Category 3

i = 112

15+20+25+30+35+40+45+50+55+60+65+70=510

OR 12/2 (15+70) = 510

500 Category 3500 Category 3

Answer

i = 3 ii22

11

Hint Sn

Formula

won’t work!

Answer 500 Category 3Answer 500 Category 3

i = 3 ii22

11

-4+-11+-20+-31+-44+-59+-76+-95

+-116 =-456

100 Category 4100 Category 4

Answer

Write the rule if

r = 6 and a1 =7

and find a10

Answer 100 Category 4Answer 100 Category 4

Write the rule if

r = 6 and a1 =7

an = 6(5)n-1

a10 = 6(5)10-1= 11,718,750

200 Category 4200 Category 4

Answer

Write the rule for

2, 10, 50, 250...

Answer 200 Category 4Answer 200 Category 4

Write the rule for

2, 10, 50, 250…

an = 2(5)n-1

300 Category 4300 Category 4

Answer

Write the 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

Find the 2 geometric means

between 3 and 648

Answer 500 Category 4Answer 500 Category 4

Find the 2 geometric means

between 3 and 648

3, , ,648

18,108

100 Category 5100 Category 5

Answer

Find the S3 for

5, 30, 180

Answer 100 Category 5Answer 100 Category 5

Find the S3 for

5+ 30+ 180=215

200 Category 5200 Category 5

Answer

Find the S5 for

10, -30, 90, -270

Answer 200 Category 5Answer 200 Category 5

Find the S5 for

10+ -30+ 90+

-270+810=610

300 Category 5300 Category 5

Answer

Find the S7 for

200,100,50...

Answer 300 Category 5Answer 300 Category 5

Find the S7 for

200+100+50+25+25/2+25/4+25/

8=396.875

400 Category 5400 Category 5

Answer

i = 1))(i-(i-3

Answer 400 Category 5Answer 400 Category 5

i = 1))(i-(i-3

3+6+12 = 21

500 Category 5500 Category 5

Answer

If you play the stock market and you earn $1600 the first day, you lose $800 the next day. On the third day you earn $400. If this pattern continues what will be your total earned (or lost) after 5 days?

Answer 500 Category 5Answer 500 Category 5

$1600+-800+400+-200 +100 = 1100

Double JeopardyDouble JeopardyFind the 3

geometric means between 2 and

1250Answer

Double Jeopardy AnswerDouble Jeopardy Answer

Find the 3 geometric means between 2 and

1250

2, , , ,1250

10,50,250

Final JeopardyFinal Jeopardy

If you play the stock market and you earn $1600 the first day, you earn $800 the next day. On the third day you earn $400. If this pattern continues on what day will you no longer make even a penny?

Answer

Final JeopardyFinal Jeopardy

1600,800,400,200,100,50,25,

25/2, 25/4,25/8, 25/16,…on the 17th day you make .02

19th day .0061

20th day .00305

sn = 1600(1/2)n-1

sn = 1600(1/2)20-1 =.00305