The answer would be: an = 10( one half )n − 1; average rate of change is negative fifteen halves.
This question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5) and point C(4,1.25).
If you insert point A to the function, an = 10( one half )^n − 1 will give a result of 10 for n=1.
For n=0, the result would be:
an = 10( one half )^n − 1
an= 10(1/2)^0-1
an= 10(1/2)^-1= 10* 2= 20
Then the average rate of change from n=0 to n=2 would be:
Rate of change= (y2-y1)/ (x2-x1)
Rate of change= (5-20)/ (2-0)= -15/2= negative fifteen halves
