Arithmetic Sequences
Recursive Equation
Geometric Sequences
Explicit Equation
Vocabulary
100
These are the next 3 terms of the arithmetic sequence 1, 4, 7, 10, 13, ...
What are 16, 19, 22.
100

What is a recursive equation for the sequence, 2, 5, 8, 11, 14, .....

a(1)= =2

an= an-1 + 3

n>2

100
These are the next 3 terms of the geometric sequence 45, 90, 180, 360, ...
What are 720, 1440, 2880
100

Given the arithmetic explicit equation below, identify the first term, and the rate of change.

an = 8 + 2(n-1)

What is, the first term is 8 and the rate of change is 2

100

If g(a) represents a sequence with a being the step #, can g(4.3) be a value? Why or why not?

No, no fractions or decimals allowed!!! There is no such thing as term # 4.3 

(term 1, term 2, term 3, term 4, term 5,... ect)

200

Whether or not this sequence is arithmetic 0, 3, 7, 12, 18, ...

What is no.

200

What is a recursive equation for the sequence 1, 6, 36, 216, 1296,......?

a1 = 1

an = an-1 * 6

N>2

200
Whether or not this sequence is geometric 7, 0.7, 0.07, 0.007, ...
What is yes.
200

Identify the first term and the common ratio in the geometric sequence equation below.

an = 4 (2)n-1

What is, the first term is 4 and the common ratio is 2.

200

This type of sequence multiplies by a growth factor in between each term.

What is geometric sequence.

300

This is the explicit formula for the arithmetic sequence -2, 5, 12, 19, ...

What is a(n)= -2+7n   n>0

300

Write a recursive equation for an arithmetic sequence whose 3rd term is 4 and 5th term is 10

a1 = -2

an = an-1 + 3

n>2

300
This is the explicit formula for the geometric sequence -5, 10, -20, 40, ...
What is a_n=-5*(-2)^(n-1)
300

Write the explicit equation for the sequence defined by the terms,  24, 12, 6, 3, 1.5, .......

What is  an = 24 (0.5)n-1

300

The number that is added or subtract to a term in order to find the next term of an arithmetic sequence

Rate of change

400
This is the missing term in the arithmetic sequence 101, __, -115, ...
What is -7
400

write a recursive equation for the following sequence

-3, 9, -27, 81, -243

a1 = -3

an = an-1 * -3

n>2

400
This is the missing term in the geometric sequence 9180, __, 255, ...
What is 1530.
400

Given the 2nd term of the sequence is 3 and the 5th term is 9, write the explicit equation.

an = 1 + 2(n-1)

400

The number that is multiplied by a term in order to find the next term of a geometric sequence

Growth Factor

500

A contractor must pay a penalty if work on a project is not completed on time. The penalty on the first day is $300. The penalty increases to $500 on the second day, to $700 on the third day, and so on. The contractor ended up having to pay a penalty of $4500. This is the number of days after the due date that the project was completed.

What is 22

500

which sequence will eventually outgrow the other?

a1 = -5                               b1 = 1

an = an-1 * 2                       bn = bn-1 + 2

sequence a because its geometric

500
Suppose you save $1 on the first day of a month, $2 the second day, $4 the third day, and so on. This is the amount of money you will set aside on the 15th day of the month.
What is $16,384
500

Determine if the two equations below represent the same sequence of numbers.  Explain how you know.

an = 3 + 6(n-1)   n>0  and      bn = -3 + 6n n>0

What is, yes sequence a and b are the same and you know because an uses the first term 3 in the equation and if you subtract the common difference of 6 you get the zero term which is -3.   Both sequence use the same common difference of 6

500

What type of functions do arithmetic and geometric sequences resemble?

What are Linear and Exponential Functions

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