Determine which of the following scenarios could be modeled by an arithmetic sequence. (Could be more than one answer)(1 point)
Arithmetic Not Arithmetic
A cane of bamboo is 30 in. tall the first week and grows 6 in. per week thereafter.
Arithmetic – A cane of bamboo is 30 in. tall the first week and grows 6 in. per week thereafter.
Not Arithmetic – A cane of bamboo is 30 in. tall the first week and grows 6 in. per week thereafter.
You find a magic penny that doubles in value every day for 30 days.
Arithmetic – You find a magic penny that doubles in value every day for 30 days.
Not Arithmetic – You find a magic penny that doubles in value every day for 30 days.
You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter
Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter
Not Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter
You keep your money in an savings account that pays you 10% interest each week.
Not Arithmetic – You keep your money in an savings account that pays you 10% interest each week.
Not Arithmetic - You keep your money in a savings account that pays you 10% interest each week.
Not Arithmetic – You keep your money in a savings account that pays you 10% interest each week.
To determine whether a scenario can be modeled by an arithmetic sequence, we need to check if there is a constant difference between consecutive terms. In an arithmetic sequence, each term is obtained by adding or subtracting a constant value from the previous term.
In the scenario of a cane of bamboo, the height is increasing by 6 inches every week. Since there is a constant difference of 6 inches, this scenario can be modeled by an arithmetic sequence.
In the scenario of finding a magic penny, the value doubles every day. Since the increase is not constant, this scenario cannot be modeled by an arithmetic sequence.
In the scenario of borrowing money and paying it back, the amount paid back is decreasing by $25 every week. Since there is a constant difference of $25, this scenario can be modeled by an arithmetic sequence.
In the scenario of keeping money in a savings account with 10% interest, the amount would increase by a varying percentage every week based on the previous balance. Since the increase is not a constant value, this scenario cannot be modeled by an arithmetic sequence.