Determine which of the following scenarios could be modeled by an arithmetic sequence. (Could be more than one answer)(4 points) Arithmetic Not Arithmetic A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. Arithmetic – A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. Not Arithmetic – A cane of bamboo is 30 inchess tall the first week and grows 6 inches 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 – A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
Arithmetic – You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
To determine if a scenario can be modeled by an arithmetic sequence, we need to check if there is a constant difference between each term.
For the given scenarios:
1. A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter.
This scenario can be modeled by an arithmetic sequence because there is a constant difference of 6 inches between each week.
2. You find a magic penny that doubles in value every day for 30 days.
This scenario cannot be modeled by an arithmetic sequence because the growth rate doubles each day, meaning there is no constant difference.
3. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter.
This scenario can be modeled by an arithmetic sequence because there is a constant difference of $25 between each week.
4. You keep your money in a savings account that pays you 10% interest each week.
This scenario cannot be modeled by an arithmetic sequence because the interest rate is based on a percentage, not a constant difference.
Therefore, the scenarios that could be modeled by an arithmetic sequence are:
- A cane of bamboo growing 6 inches per week
- Borrowing $350 and paying back $25 each week.
The scenarios that could be modeled by an arithmetic sequence are:
1. A cane of bamboo is 30 inches tall the first week and grows 6 inches per week thereafter. (Arithmetic)
2. You borrow $350 from a friend the first week and pay the friend back $25 each week thereafter. (Arithmetic)
The other scenarios are not arithmetic sequences:
1. You find a magic penny that doubles in value every day for 30 days. (Not Arithmetic)
2. You keep your money in a savings account that pays you 10% interest each week. (Not Arithmetic)