I need some help answering this question.

Question

 

I know that graph A fits the geometric sequence of 1/3, but I can't figure out if the other graphs  also follow this patern.

Answer 1

Step 1:

The geometric sequence of ratio .

The n ^th term of the geometric series is , where a is the first term and r  is the common ratio.

Common ratio .

Here the common ratio is .

n ^th term of the geometric series with ratio is .

Consider the graph (A).

The points on the graph (A) are and .

Check the common ratio for each and every point.

Consider the points .

Here the n ^th term is 3 and (n - 1)^th term is 9 then the common ratio is .

For the points , the common ratio is .

For the points , the common ratio is .

So here the graph (A) is the geometric sequence of ratio .

Step 2:

Check for rest of the graphs.

Consider the graph (B).

The points on the graph (B) are and .

Check the common ratio for each and every point.

For the points , the common ratio is .

For the points , the common ratio is .

For the points , the common ratio is .

So here the graph (B) is the geometric sequence of ratio .

Answer 2

Step 3:

Consider the graph (C).

The points on the graph (C) are and .

Check the common ratio for each and every point.

For the points , the common ratio is .

For the points , the common ratio is .

For the points , the common ratio is .

So here the graph (C) is the geometric sequence of ratio .

Step 4:

Consider the graph (D).

The points on the graph (C) are and .

Check the common ratio for each and every point.

For the points , the common ratio is .

For the points , the common ratio is .

For the points , the common ratio is .

So here the graph (D) is not the geometric sequence of ratio .

Graph (A), (B) and (C) are the exponential functions correspond to geometric sequence of ratio .

Graph (A), (B) and (C) are the correct answers.

Solution:

Graph (A), (B) and (C) are the correct answers.