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

Formula: ##a_n = -3n + 11##
: ##N##
By definition an arithmetic sequence is of the form…
##a_n = a_1 + (n-1)d##
Where ##n## is the term number and ##d## is the common difference.
We’re told that ##a_1 = 8## and that ##a_2 = 5## so we have the equation…
##a_2 = a_1 + (2 -1) d##
##5 = 8 + d##
##-3 = d##
##d = -3##
So our explicit formula is…
##a_n = 8 – ((n-1) * 3)##
##a_n = 8 – (3n – 3)##
##a_n = -3n + 11##
The domain for all is ##n in N## where ##N## denotes the natural numbers (i.e. ##N = {1, 2, 3, 4, …..}##