Question

Josh is picking flowers in the garden. He picked 9 flowers from the first bush, 16 flowers from the second bush, 25 flowers from the third bush, and 36 flowers from the fourth bush. What kind of sequence is this?

Answer 1

To determine the kind of sequence formed by the number of flowers Josh picked from the bushes, we can observe the numbers: 9, 16, 25, and 36.

Let's examine the differences between the consecutive terms:

- The difference between the second and first term (16 - 9) is 7.
- The difference between the third and second term (25 - 16) is 9.
- The difference between the fourth and third term (36 - 25) is 11.

So we have the differences: 7, 9, and 11.

Next, let's look at the differences of these differences:

- The difference between 9 and 7 is 2.
- The difference between 11 and 9 is 2.

The second differences are constant (both equal to 2). This implies that the sequence of the number of flowers picked is a quadratic sequence.

In summary, the numbers 9, 16, 25, and 36 form a quadratic sequence.