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
(5 points)

an = 20( one half )n − 1; average rate of change is fifteen halves
an = 10( one half )n − 1; average rate of change is fifteen halves
an = 20( one half )n − 1; average rate of change is negative fifteen halves
an = 10( one half )n − 1; average rate of change is negative fifteen halves

Answer 1

PLS I NEED HELP

Answer 2

notice how each consecutive term takes the previous term and multiplies it by 1/2. therefore, the rate of change is r = 1/2.

10 --> 5 --> 2.5 --> 1.25

the first point on the **graph** is (2,10), but for geometric sequences, we want a1, or the term at x = 1. to do this, we work backwards from (2,10). multiplying by 2 gives us (1,20) as the first term, or a1 = 20.

finally, fill in the formula:

an = (a1) * (r) ^ (n-1)

Answer 3

for the average rate of change:

between n = 1 and n = 3, the formula is:

\[\frac{ f(3)-f(1) }{ 3-1 }\]
use the graph to find the f(3) and f(1) values