Unit 7 Review

Arithmetic,Geometric or Neither

100

2,6,18,54, ...

Geometric

200

5,15,25,35, ...

Arithmetic

300

1/2,13/2,25/2,37/2, ...

Arithmetic

400

25,225,2025,18225, ...

Geometric

500

1,5,9,32, ...

Neither

Common Ratio

100

9,54,324,1944, ...

r=6

200

17,34,68,136, ...

r=2

300

2,30,450,6750, ...

r=15

400

8,160,3200,64000, ...

r=20

500

18,72,288,1152, ...

r=4

Common Difference

100

96,156,216,276, ...

d=60

200

10,36,62,88, ...

d=26

300

77,165,253,341, ...

d=88

400

-39,17,73,129, ...

d=56

500

-36,-14,8,30, ...

d=22

Recursive,Explicit,Common Difference(Arithmetic)

100

8,17,26,35, ...

Recursive:?

Explicit:?

d=?

Find a12

d=9

Recursive: a1=8    

                an=an-1+9

Explicit: an=a1+d(n-1)

            an=8+9(n-1)

            an=8+9n-9

            an=9n-1

a12=9(12)+1

a12=109

200

a8=11, d=4

Find a1

Explicit:?

Recursive:?

Find a33

Explicit: an=-1+4(n-1)

             an=-1+4n-4

             an=4n-5

Recursive: a1=-1

                an=an-1+4

a33=4(33)-5

a33=127

300

a4=-3, d=2

Find a1

Explicit:?

Recursive:?

Fnd a27

Explicit: an=-11+2(n-1)

             an=-11+2n-2

             an=2n-13

Recursive:a1=-11

               an=an-1+2

a27=2(27)-13

a27=41

400

34,41,48,55, ...

d=?

Recursive:?

Explicit:?

Find a17

d=7

Recursive: a1=34

                an=an-1+7

Explicit: an=34+7(n-1)

             an=34+7n-7 

             an=7n+27

a17=7(17)+27

a17=146

500

a35=-16, d=3

Find a1

Recursive:

Explicit:

Find a10

Recursive: a1=-118

                an=an-1+3

Explicit: an=-18+3(n-1)

             an=-18+3n-3

              an=3n-21

a10=3(10)-21

a10=9

Recursive,Explicit,Common Ratio(Geometric)

100

4,32,256,2048, ...

r=?

Recursive:?

Explicit:?

Find a5

r=8

Recursive: a1=4

                an=an-1(8)

Explicit: an=4(8)^n-1

a5=4(8)^5-1

a5=16,384

       

200

6,18,54,162, ...

r=?

Recursive:?

Explicit:?

Find a9

r=3

Recursive: a1=6

                an=an-1(3)

Explicit: an=6(3)^n-1

a9=6(3)^9-1

a9=39,366

300

a2=-40, r=-8

Find a1

Recursive:?

Explicit:?

-40=a1(-8)^2-1

-40=a1(-8)^1

-40/-8=a1(-8)/-8

a1=5

Recursive: a1=5

                an=an-1(-8)

Explicit: an=5(-8)^n-1

400

a4=-108, r=3

Find a1

Recursive:?

Explicit:?

-108=a1(3)^4-1

-108=a1(3)^3

-108/27=a1(27)/27

a1=-4

Recursive: a1=-4

                an=an-1(3)

Explicit: an=-4(3)^n-1

500

2,26,338,4394, ...

r=?

Recursive:?

Explicit:?

Find a4

r=13

Recursive: a1=2

                an=an-1(13)

Explicit: an=2(13)^n-1

a4= 2(13)^4-1

a4=4,394