Arithmetic Sequence Review

Find common difference

100

Find the Common Difference for this sequence:

1,2,3,4,...

d=1

200

Find the Common Difference for this sequence:

4,12,20,...

d=8

300

Find the Common Difference for this sequence:

-3,-6,-9,...

d=-3

400

Find the Common Difference for this sequence:

f(1)=-67

f(2)=-60

f(3)=-53

d=7

500

Find the Common Difference for this sequence:

f(1)=8

f(2)=-12

f(3)=-32

d=-20

Create Recursive Formula

100

Create the recursive formula given the following information:

f(1)=7

d=-3

Recursive Formula:

f(n)=f(n-1)-3

200

Create the recursive formula given the following information:

f(1)=7

d=43

Recursive Formula:

f(n)=f(n-1)+43

300

Create the recursive formula given the following sequence:

4,8,12,...

Recursive Formula:

f(n)=f(n-1)+4

400

Create the recursive formula given the following information:

f(1)=7

f(2)=10

Recursive Formula:

f(n)=f(n-1)+3

500

Create the recursive formula given the following information:

f(1)=10

f(2)=-30

Recursive Formula:

f(n)=f(n-1)-40

Create Explicit Formula

100

Create the Explicit Formula given the following information:

f(1)=4

d=5

Explicit Formula:

f(n)=5(n-1)+4

OR

f(n)=5n-1

200

Create the Explicit Formula given the following information:

f(0)=9

d=-3

Explicit Formula:

f(n)=-3n+9

OR

f(n)=-3(n-1)+6

300

Create the Explicit Formula given the following information:

f(0)=-3

f(1)=2

f(2)=7

Explicit Formula:

f(n)=5n-3

OR

f(n)=5(n-1)+2

400

Given the explicit formula from f(1) find the explicit formula with f(0):

f(n)=5(n-1)+7

Explicit Formula:

f(n)=5n+2

500

Given the explicit formula for f(0) find the explicit Formula from f(1):

f(n)=-3n+8

Explicit Formula:

f(n)=-3(n-1)+5

Find Terms

100

Given the first term and the difference find the first five terms: 

f(1)=23

d=4

First five terms:

23,27,31,35,39

200

Given the first term and the difference find the first five terms: 

f(1)=-23

d=-13

First five terms:

-23,-36,-49,-62,-75

300

Given the first and the third term, find the second term and the difference:

f(1)=27

f(3)=31

Difference and second term:

d=2

f(2)=29

400

Given the first term and the recursive formula find the first times:

f(n)=f(n-1)+7

f(1)=20

First 5 Term:

20,27,34,41,48

500

Given the explicit formula find the first 5 terms: 

f(n)=3n-7

First 5 terms:

-4,-1,2,5,8

Random

100

a₁ is another way of saying what?

The First Term!

200

What is the definition of an Arithmetic Sequence?

A pattern of numbers where the difference between the numbers remains constant.

300

Use the explicit formula to the 47^th term:

f(n)=5n+19

Answer:

f(n)=254

400

Given the 7^th and 9^th term of an arithmetic sequence find the difference:

f(7)=24

f(9)=84

Answer:

d=30

500

When we don't know what the sequence looks like or if we are missing terms, what should we create to help us see the pattern?

A Table!!!