Question

23.
Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.

–9, –4, 1, 6, . . .

Answer 1

To find the pattern in the sequence –9, –4, 1, 6, let’s first examine the differences between successive terms:

- From –9 to –4, the difference is:
\(-4 - (-9) = -4 + 9 = 5\)

- From –4 to 1, the difference is:
\(1 - (-4) = 1 + 4 = 5\)

- From 1 to 6, the difference is:
\(6 - 1 = 5\)

We can see that the difference between each pair of successive terms is consistently 5.

Using this pattern, we can find the next two numbers by continuing to add 5 to the last number (6):

- Next number:
\(6 + 5 = 11\)

- Following number:
\(11 + 5 = 16\)

Thus, the next two numbers in the pattern are **11** and **16**.