Find an explicit formula for the arithmetic sequence

81,54,27,0, ...

an = - 27n + 108.

Step-by-step explanation:

The first term a1 = 81 and the common difference d = 54-81 = - 27. (Also 27 - 54 = - 27 and 0 - 27 = - 27).

The explicit formula is

an = a1 + d (n - 1)

= 81 - 27 (n - 1)

= - 27n + 81 + 27

= - 27n + 108.