Question

Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.

–3, 9, –27, 81, . . .


multiply the previous term by 3; 243, 729


subtract 12 from the previous term; –243, 729


multiply the previous term by –3; –243, 729


add 12 to the previous term; 69, 57

Answer 1

To begin, let's examine the given sequence: –3, 9, –27, 81.

We will use inductive reasoning to identify the pattern:

1. Starting with –3:
- The first term is –3.

2. Second term (9) is obtained by multiplying the first term (–3) by –3:
- –3 × (–3) = 9.

3. Third term (–27) is obtained by multiplying the second term (9) by –3:
- 9 × (–3) = –27.

4. Fourth term (81) is obtained by multiplying the third term (–27) by –3:
- –27 × (–3) = 81.

From this, we see a clear pattern: each term is obtained by multiplying the previous term by –3.

To find the next two numbers in the sequence:

- Next term after 81:
- 81 × (–3) = –243.

- Next term after –243:
- –243 × (–3) = 729.

So the next two numbers in the pattern are **–243** and **729**.