Question

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 2, 10, point 3, 5, point 4, 2.5, and point 5, 1.25

Answer 1

• geometric sequence with initial value 20 and common ratio 1/2
• average rate of change on [1, 3] = -7.5

Explanation:

(a) The given points have sequential values of x and values of y that are each 1/2 the value before. The common ratio tells us the sequence is a geometric sequence.

(b) The first given point is (2, 10), so extrapolating backward, we determine the previous point to be ...

... (2-1, 10/(1/2)) = (1, 20)

Thus, we have enough information to determine the average slope between n=1 and n=3.

... (difference in y)/(difference in n) = (5 -20)/(3 -1) = -15/2 = -7.5