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QUESTION

# 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, .....}