1.

Question

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

–5, –10, –20, –40, . . .

Answer 1

To identify the pattern in the sequence –5, –10, –20, –40, we can observe how each number relates to the preceding number.

1. First, look at the relationship between consecutive numbers:
   • –10 is obtained by multiplying –5 by 2 (–5 * 2 = –10).
   • –20 is obtained by multiplying –10 by 2 (–10 * 2 = –20).
   • –40 is obtained by multiplying –20 by 2 (–20 * 2 = –40).

Based on this pattern, each number in the sequence is obtained by multiplying the previous number by 2.

2. To find the next two numbers:
   • The next number after –40 is –40 * 2 = –80.
   • The number after that is –80 * 2 = –160.

Therefore, the next two numbers in the pattern are –80 and –160.