Sequences

Vocabulary

100

An arithmetic/linear sequence grows or decays according to which operations? 

Adding or a subtracting a number

200

A geometric/exponential sequence grows or decays by which operations?

multiplication or division

300

A function that moves step by step

Recursive function

400

A function that can be used to find any number in the sequence

explicit function

Arithmetic Sequences

100

What do you need in order to create a recursive arithmetic function?

common difference, a₁ and formula for a_n

200

What do you need in order to create an explicit arithmetic function?

common difference, a_0, and a_n

300

Write a recursive function for 1,4,7,10......

a₁=1

a_n=a_n-1+3

400

Write an explicit function for 1,4,7,10.....

a_n=3n-2

Geometric Sequences

100

What do you need in order to create a recursive geometric function?

common ratio, a₁, and formula for a_n

200

What do you need in order to create an explicit geometric function?

common ratio, a₀, and a_n

300

Create a recursive function for the following sequence: 3,9,27,81,.........

f(1)=3

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

400

Create an explicit function for the following sequence: 3,9,27,81,.........

a_n=1*(3)ⁿ

Finding values

100

Find the third term of the sequence:

a₁=3

a_n=a_n-1+5

13

200

Find the fourth term of the sequence:

a_n=4n+2

18

300

Find the third term of the sequence:

a₁=5

a_n=6*a_n-1

180

400

Find the second term of the sequence:

a_n=36*(1/2)ⁿ

9