Question

URGENT!!!!!!

Answer 1

Answer: Choice B

a_n = 10(1/2)^(n-2) is the nth term

average rate of change = -35/3

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Explanation:

Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.

If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.

Use the slope formula to find the slope of the line through (0,40) and (3,5)

m = (y2-y1)/(x2-x1)

m = (5-40)/(3-0)

m = -35/3

The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3

The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.

In other words, 20(1/2)^(n-1)  is equivalent to 10(1/2)^(n-2) when n starts at n = 1.