Question

The image shows three sets of stuffed bears. Each set represents a term of the sequence (1, 4, 7, . . .) What is the next term in the sequence?
Describe the domain of the sequence. Describe the range of the sequence btw da numbers represents how many stuffed bears are in each set. (u dont need to see da image)

Answer 1

Next term = 10

You add 3 to each term to get the next

1+3 = 4

4+3 = 7

7+3 = 10

etc etc

The domain of the sequence is 1,2,3,4,... basically the set of positive whole numbers. This is known as the set of natural numbers or counting numbers. We don't include 0. The domain is the set of possible inputs for 'n' in the formula mentioned below.

The range is the sequence of values shown.

The formula to generate the sequence is

an = 3n-2

as shown by these steps below

an = a1 + d(n-1)

an = 1 + 3(n-1)

an = 1+3n-3

an = 3n-2

To get any term you want, plug in a whole number for n. For example, plug in n = 4 to get...

an = 3n-2

a4 = 3*4-2

a4 = 12-2

a4 = 10

Showing that the fourth term is 10 as found earlier above.