Arithmetic and Geometric Sequences and Series

Question 1

What is a Sequence?

Answer 1

An ordered list of numbers

Question 2

What is an arithmetic sequence?

Answer 2

Question 3

What is a common difference?

Answer 3

the number you repeatedly add to get the next term in an arithmetic sequence

Question 4

How do you find the common difference?

Answer 4

Subtract a term by the previous term.
Example:

Question 5

What is a geometric sequence?

Answer 5

In an geometric sequence we always multiply by the same amount to get from one term to the next. The amount we multiply by is known as the common ratio and we use the letter r to refer to it.

Question 6

What is the common ratio?

Answer 6

The number you repeatedly multiply in order to get the next term in the geometric sequence.

Question 7

How do you find the common ratio

Answer 7

divide a term by the previous term

Question 8

What do the variables represent in these formulas?

Answer 8

Question 9

All these formulas require the first term- what should you do if you are not given the first term?

Answer 9

Question 10

If a problem mentions “doubling” what is the common ratio?

Answer 10

r=2

Question 11

What is the common ratio?

Each year, the size of the iceberg is 75% that of the previous year.

Answer 11

Question 12

What is the common ratio?
Each year, the employee receives a 5% raise.

Answer 12

Question 13

What is the common ratio?
Each day, the value of the car decreases by 10%

Answer 13