Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5? 20 pts.

Answer 1

`a_n = 11 - 3n`

Step-by-step explanation

The explicit rule for an arithmetic sequence is given by:

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

It was given that:

`a_1 = 8`

and

`a_2 = 3`

The common difference is

`d = 5 - 8 = - 3`

We plug in the values into the explicit formula to get,

`a_n = 8+ - 3(n - 1)`

Expand to get,

`a_n = 8 - 3n + 3`

The explicit rule is

`a_n = 11 - 3n`