Arithmetic sequences (IBDP AA+AI)

Multiple Choice

Which of the following best describes the significance of studying arithmetic progressions and financial mathematics in real life?

• They help in understanding patterns and making financial decisions.

• They are only useful for solving classroom problems.

• They are mainly used for historical analysis.

• They are not relevant to daily life.

Multiple Choice

What is the common difference in the arithmetic sequence shown, and how does it affect the progression of terms?

• The common difference is 3, and it increases each term.

• The common difference is -3, and it decreases each term.

• The common difference is 7, and it increases each term.

• The common difference is -7, and it decreases each term.

Open Ended

Explain how the formula for the general term of an arithmetic sequence is derived from its definition.

Multiple Choice

Which steps are involved in solving for the first term and common difference of an arithmetic sequence when given two non-consecutive terms?

• Set up simultaneous equations, eliminate d, substitute to find u1.

• Set up simultaneous equations, eliminate u1, substitute to find d.

• Set up simultaneous equations, add the equations, substitute to find d.

• Set up simultaneous equations, multiply the equations, substitute to find u1.

Multiple Choice

Find the first 6 terms of the sequence.

• 13, 19, 25, 31, 37, 43

• 7, 13, 19, 25, 31, 37

• 1, 7, 13, 19, 25, 31

• 7, 12, 17, 22, 27, 32

Multiple Choice

What is the common difference of this sequence?

• 4
• 3
• 7
• 1

Multiple Choice

What is the explicit equation for the arithmetic sequence in the table?

• $$y=4x+3$$  

• $$y=3x+4$$  

• $$y=4\left(3\right)^x$$  

• $$y=3x+1$$  

Multiple Choice

• 149
• 11,200
• 5,600
• 140

Multiple Choice

Find the sum of the arithmetic series using a formula.

• 516, 240

• 516,242

• 116, 242

• 506, 242

Multiple Choice

You rented the carpet cleaner for 5 hours, how much would you pay?

• 24

• $40
• $42
• $38

Multiple Choice

Find the sum of the first 15 terms of the arithmetic series

• A

• B

• C

• D

Multiple Choice

Which of the following statements correctly distinguishes between arithmetic and geometric models in financial applications?

• Arithmetic models use a fixed percentage rate change, while geometric models use a fixed amount change.

• Arithmetic models use a fixed amount change, while geometric models use a percentage rate change.

• Both models use a fixed amount change.

• Both models use a percentage rate change.

Multiple Choice

Select the correct answer

• A

• B

• C

• D

Multiple Choice

If a certain bacteria doubles every hour, how many bacteria could be found in the sample after 5 hours if there were 24 to start with?

• 240
• 7776
• 768
• 384

Multiple Choice

What does the n stand for in this formula?

• Initial amount

• Final amount

• Rate

• Time

• The number of times compounded per year

Open Ended

Explain the difference between the arithmetic approximation and the geometric model when adjusting for inflation in financial calculations.

Multiple Choice

Which variables must be entered as negative values in a financial calculator when representing cash outflow?

• N (Number of periods)

• I% (Interest rate)

• PV (Present Value)

• FV (Future Value)

Multiple Choice

A bank is offering 7% annual compound interest on a savings account.  If you deposit $1,500, how much interest will you earn in three years?

• $1837.56
• $337.56
• $30000
• $31500

Fill in the Blank

In sequences (Un), n must always be a ___ integer.

Multiple Choice

The first three terms of an arithmetic sequence are x+1, 3x, and 6x-5. What is the value of x?

• 2

• 4

• 6

• 8

Multiple Choice

What do you have to multiply the first equation by to have the x's be opposite and the same?

• 3

• 2

• -2

• -3

Multiple Choice

Which of the following best describes the difference between arithmetic and geometric financial modeling?

• Arithmetic models use rate change, geometric models use fixed change.

• Arithmetic models use fixed change, geometric models use rate change.

• Both models use fixed change.

• Both models use rate change.

Open Ended

How do you think understanding arithmetic progressions and financial mathematics can be useful in real-life situations?

Multiple Choice

Which step in the analytical progression involves learning about summation notation and series formulae?

• Define

• Formalize

• Aggregate

• Apply