12.

Question

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

1, 4, 7, 10, . . .

Answer 1

To describe the pattern in the sequence 1, 4, 7, 10, we can look at the differences between consecutive terms:

• The difference between 4 and 1 is 3.
• The difference between 7 and 4 is 3.
• The difference between 10 and 7 is 3.

We see that each term increases by 3 from the previous term.

Based on this pattern, we can determine the next two numbers:

1. The next number after 10 is \(10 + 3 = 13\).
2. The number after 13 is \(13 + 3 = 16\).

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