Question

(Worth 30 points) What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3? (Answers are attached as a picture)

Answer 1

`a_n=5-2(n-1)`, all integers where n≥1

Explanation:

we know that

The explicit equation for an arithmetic sequence is equal to

`a_n=a_1+d(n-1)`

a_n is the th term

a_1 is the first term

d is the common difference

n is the number of terms

we have

`a_1=5\\a_2=3`

Remember that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference.

To find out the common difference subtract the first term from the second term

`d=a_2-a_1=3-5=-2`

substitute the given values in the formula

`a_n=5-2(n-1)`

The domain is all integers for
`n\geq 1`