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# 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, .....}##