Answer:
16. -2 . . . thousand
17. a = 20 -2(m -1) . . . . . a = amount (thousands); m = month
18. a(11) = 0
Explanation:
Given a plan to pay down a credit card so that the amounts remaining in months 1, 2, 3 are 20, 18, 16 thousands, you want to know the common difference, the explicit formula, and the amount to be paid in month 11.
16. Common difference
The difference between remaining amounts is ...
18 -(20) = -2 . . . . thousands
It is the same for each pair of successive months, so is a common difference.
17. Explicit formula
The sequence of remaining amounts is an arithmetic sequence. The explicit formula for an arithmetic sequence can be written ...
a(n) = a(1) +d(n -1)
We have first term a(1) = 20, and common difference d = -2, so the explicit formula for the remaining amount in thousands can be ...
a(m) = 20 -2(m -1) . . . . . . where m is the month number
18. Month 11
The amount remaining in month 11 is found using the above formula:
a(11) = 20 -2(11 -1) = 0
The remaining amount to be paid in month 11 is 0.