Question

a school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 40 dumpster loads of waste removed. in wee 10,there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.

Answer 1

Since it is given that the reduction in the amount of waste each week is linear, it is conclusive that these data are also in arithmetic sequence. First, determine the common difference (d)
                                 d = (a10 - a5) / (10 - 5)
Subsituting the known values,
                                d = (30 - 40) / 5 = -2
To determine any term (at) of the arithmetic sequence,
                            at = a1 + (n - 1) x d 
Solve for a1 by using either the given a5 or a10,
                            40 = a1 + (5 -1) x -2     ; a1 = 48
The equation becomes, 
                                 at = 48 + -2(n -1)