You budget $100 for parking each month. Each day you use the downtown parking lot, it costs you $5. Write a rule to represent the amountof money left in your monthly budget as an arithmetic sequence. How much money is left in your budget after you have used the downtown parking lot 11 times this month?
To write a rule that represents the amount of money left in your monthly budget as an arithmetic sequence, we need to find the common difference, which is the amount of money being deducted each time.
In this case, each day you use the downtown parking lot, it costs you $5. Therefore, the common difference is -$5 (negative because it represents money being deducted).
Now, let's set up the rule to represent the amount of money left in your budget after using the parking lot. Let "n" represent the number of times you have used the parking lot:
aₙ = a₁ + (n-1)d
where:
aₙ is the nth term of the sequence (amount of money left)
a₁ is the first term of the sequence (initial amount of money, which is $100)
n is the number of times you have used the parking lot (11 in this case)
d is the common difference (-$5)
Plugging in the values into the formula:
aₙ = 100 + (11 - 1)(-5)
= 100 + 10(-5)
= 100 - 50
= $50
Therefore, after using the downtown parking lot 11 times, you would have $50 left in your budget.
To represent the amount of money left in your monthly budget as an arithmetic sequence, we can start with $100 and deduct $5 for each use of the downtown parking lot.
The rule can be written as:
a(n) = 100 - 5n
Where "n" represents the number of times the downtown parking lot has been used.
To find out how much money is left in your budget after using the downtown parking lot 11 times, we can substitute the value of "n" as 11 into the equation:
a(11) = 100 - 5 * 11
a(11) = 100 - 55
a(11) = 45
Therefore, after using the downtown parking lot 11 times this month, you would have $45 left in your budget.