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

ANSWER

$a_n = 11 - 3n$

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

$a_n = 11 - 3n$