Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?

Answer 1

a1=8 d=-3
so an=a1+(n-1)d = 8+(n-1)(-3) = 8-3n+3 =11-3n

Answer 2

`a_(n)= 11 -3n` , domain ( -∞,∞).

Explanation:

Given: An arithmetic sequence with a first term of 8 and a second term of 5.

To find : What are the explicit equation and domain

Solution : We have given that First term = 8.

Second term = 5.

By the explicit equation formula :
`a_(n)= a_(1) +(n-1)d`

`a_(n)` = the nth term in the sequence

.

`a_(1)` = the first term in the sequence

n = the term number

d = the common difference.

Common difference = second term - first term .

5 - 8 = -3

Then ,
`a_(n)= 8 +(n-1)(-3)`.

`a_(n)= 8 -3n +3`.

`a_(n)= 11 -3n`.

Therefore,
`a_(n)= 11 -3n` and domain domain ( -∞,∞).