Question

use inductive reasoning to describe the pattern. then find the next two numbers in the pattern. –9, –4, 1, 6, . . . multiply the previous term by 5; 11, 150 multiply the previous term by 5; 30, 150 add 5 to the previous term; 11, 16 subtract 5 from the previous term; 1, –4

Answer 1

5 is added to each number to create the next number. The next 2 numbers are 11 and 16.

Answer 2

For this case we have the following sequence:

`-9, -4, 1, 6...`

We observe that we have an arithmetic sequence.

This is because each term has a common difference.

The common difference is:

`d = -4 - (- 9) = - 4 + 9 = 5\\d = 1 - (- 4) = 1 + 4 = 5\\d = 6-1 = 5`

Therefore the following two terms are:

`6 + 5 = 11\\11 + 5 = 16`

Answer:

Add 5 to the previous term; 11, 16