Alg2 Unit 1:Sequences

Recursive

100

In the following recursive definition, what is the first term and the growth factor:

f(1)=5, f(n)=f(n-1)*3  for n>2

1st term is 5

Growth Factor is 3

200

What is the initial step number in the following recursive definition:

f(0)=2, f(n)=f(n-1)*3  for n>1

Starts with step 0

300

Write the first 5 terms of the following recursive sequence:

f(1)=5, f(n)=f(n-1)*2  for n>2

5, 10, 20, 40, 80, ...

400

Write a recursive definition for the following sequence:

step 1: 3

step 2: 7

step 3: 11

step 4: 15

step 5: 19

f(1)=3, f(n)=f(n-1)+4  for n>2

500

Write a recursive definition for the geometric sequence:

f(0)=4   f(1)=12

f(0)=4,  f(n)=f(n-1)*3   for n>1

Nth Term

100

What is the growth factor in the following Nth term definition:

f(n)= 5(2)ⁿ  for n>0

growth factor is 2

200

Is the following Nth term definition a geometric or arithmetic sequence:

f(n)=3+4(n-1)  for n>1

Arithmetic

300

Write an N^th term definition for the following sequence:

step 1: 120

step 2:  60

step 3:  30

step 4:  15

step 5:  7.5

f(n)=120(1/2)^n-1   for n>1

400

Write an N^th term definition for the following arithmetic sequence:

f(0)=30   f(1)=15

f(n)=30-15n   for n>0

500

Write an N^th term definition for the following sequence:

f(1)=4,  f(2)=9,   f(3)=14,   f(4)=19,   f(5)=24

f(n)=4+5(n-1)   for n>1

Arithmetic

100

What is the rate of change for the following sequence:

80, 65, 50, 35, 20, ...

rate of change is subtracting 15

200

Write a recursive definition for the following arithmetic sequence:

7, 3, -1, -5, -9, ...

f(1)=7,  f(n)=f(n-1)-4   for n>2

OR

f(0)=7,  f(n)=f(n-1)-4  for n>1

300

Write an N^th term definition for the following arithmetic sequence:

f(0)=-7   f(1)=-2   

f(n)=-7+5n  for  n>0

400

Write an N^th term sequence for the following arithmetic sequence:

f(1)=2

f(2)=-6

f(3)=-14

f(4)=-22

f(n)=2-8(n-1)   for n>1

500

Write a recursive definition for the following arithmetic sequence:

f(1)=25    f(2)=28

f(1)=25,  f(n)=f(n-1)+3   for n>2

Geometric

100

What is the growth factor of the following sequence:

6, 18, 54, 162, ...

growth factor is 3

200

What is the growth factor of the following geometric sequence:

630, 210, 70, 70/3, ...

growth factor 1/3

300

Write an N^th term definition for the following sequence:

f(1)=244

f(2)=122

f(3)=61

f(4)=30.5

f(n)=244(1/2)^n-1    for  n>1

400

What is the growth factor of the following sequence:

5, 6.5, 8.45, 10.985, ...

growth factor is 1.3

500

What is the growth factor of the following sequence:

6, 9, 13.5, 20.25, ...

growth factor is 1.5

Sequences

100

Is the following sequence arithmetic, geometric, or neither?

10, 23, 36, 49, 62, ...

Arithmetic

200

Is the following sequence arithmetic, geometric, or neither?

64, 16, 4, 1, ...

Geometric

300

Is the following sequence arithmetic, geometric, or neither?

4, 5, 7, 10, 14, ...

Neither

400

Find the 22^nd term of the following geometric definition:

f(n)=3(2)^n-1    for n>1

6,291,456

500

Write an N^th term definition for the following sequence:

f(1)=3,   f(2)=8 ,  f(3)=15,    f(4)=24,   f(5)=35

f(n)=n(n+2)   for n>1