Question

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

1, 4, 7, 10, . . .


multiply the previous term by 3; 30, 90


subtract 3 from the previous term; 7, 4


multiply the previous term by 3; 13, 90


add 3 to the previous term; 13, 16

Answer 1

Let's analyze the given sequence: 1, 4, 7, 10, ...

To describe the pattern:

1. **Inductive Reasoning**: We can see that the difference between consecutive terms is constant:
- \( 4 - 1 = 3 \)
- \( 7 - 4 = 3 \)
- \( 10 - 7 = 3 \)

We observe that each term is obtained by adding 3 to the previous term.

2. **Pattern Identification**:
- The pattern can be described as: each term is 3 more than the previous term.

3. **Finding the Next Two Numbers**:
- To find the next terms in the sequence:
- Next term after 10: \( 10 + 3 = 13 \)
- Next term after 13: \( 13 + 3 = 16 \)

Thus, the next two numbers in the pattern are **13 and 16**.