Answer:
Part A: [tex]S_{n} = 12 + 7(n - 1)[/tex]
Part B: $131
Part C: $1314
Step-by-step explanation:
Ethan is saving money in his piggy bank for his upcoming trip to Disney World. On the first day, he put in $12 and plans to add seven more dollars each day.
Part A:
On the first day, he puts $12 in the piggy bank.
On the second day, he deposited $7 in it. So, after second day he has (12 + 7) = $19.
On the third day, he deposited $7 more in it. So, after third day he has (19 + 7) = $26.
In this way, the savings in the piggy bank are growing in an arithmetic sequence with first term $12 and a common difference $7.
Therefore, the explicit formula that can be used to find the amount of money saved on any given day is given by
[tex]S_{n} = 12 + 7(n - 1)[/tex]
Part B:
Putting n = 18, we get the money that he will have on the 18th day, is given by [tex]S_{18} = 12 + (18 - 1) 7 = 131[/tex] dollars.
Part C:
The Disney trip is in 187 days from the day he started saving. Then he will have after 187 days [tex]S_{187} = 12 + (187 - 1)7 = 1314[/tex] dollars. (Answer)
