Review Exponential Functions Geometric and Arithmetic Sequence

Does the following table represent a geometric sequence or an arithmetic? Explain 

• geometric, it has a constant rate

• geometric, it has a constant percentage

• arithmetic, it has a constant rate

• arithmetic, it has a constant percentage

If a geometric sequence is graphed, which of the following will best model the shape of the graph?

• Linear

• Exponential

• Quadratic

If an arithmetic sequence is graphed, which of the following will best model the shape of the graph?

• Linear

• Exponential

• Quadratic

Which kind of sequence has a common ratio?

• Arithmetic

• Geometric

Which kind of sequence has a common difference?

• Arithmetic

• Geometric

What kind of sequence is illustrated below?

400, 200, 100, 50, 25, ...

• Arithmetic

• Geometric

• Neither

Which sequence is an arithmetic sequence?

• 3, 6, 2, 7, ...

• 3, 6, 12, 24, ...

• 3, 6, 10, 15, ...

• 3, 7, 11, 15, ...

Create the formula for the geometric sequence.

• a_n = 2(-5)^n-1

• a_n = -2(-5)^n-1

• a_n = -2(5)^n-1

• a_n = 2(5)^n-1

Create the formula for the arithmetic sequence.

-10, -3, 4, 11, ...

• a_n = 17 - 7n

• a_n = -17 + 7n

• a_n = -17 - 7n

• a_n = 17 + 7n

The population of a city is decreasing by 3% every year. If the population is 125,000 in the 1st year, how many will remain in the 10th year?

(Hint 1: Think of 3% as a decimal.)

(Hint 2: This is an example of exponential decay. Which type of sequence represents exponential functions?)

• 92,178 people

• 95,029 people

• 167,990 people

• 163,096 people