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 …..}##