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 .

Here .

n^th term of the geometric series is .

Consider the graph (A).

The points on the graph (A) are and .

Find common ratio for each and every point.

For the points , 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 .

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 .

Find 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 .

Step 3:

Consider the graph (C).

The points on the graph (C) are and .

Find 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 .

Find 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.