Question

Which of the following is the graph of the sequence 3, -6, 9, -18, 36?

a) A linear graph with a positive slope.
b) An exponential graph that decreases.
c) An exponential graph that increases.
d) A constant graph at 3.

Answer 1

The graph of the sequence 3, -6, 9, -18, 36 is best represented by an exponential graph that increases.

Step-by-step explanation:

The graph of the sequence 3, -6, 9, -18, 36 is best represented by option (c) An exponential graph that increases.

An exponential graph is one that grows or decays at an increasing or decreasing rate. In this sequence, each term is obtained by multiplying the previous term by -2. Therefore, the sequence is increasing but in an exponential way.

For example:

• The first term is 3
• The second term is -6, which is obtained by multiplying 3 by -2
• The third term is 9, which is obtained by multiplying -6 by -2
• The fourth term is -18, which is obtained by multiplying 9 by -2
• The fifth term is 36, which is obtained by multiplying -18 by -2

As you can see, each term is obtained by multiplying the previous term by -2, demonstrating exponential growth.