Question

which word best describes this formula for the sequence $a_n$?
$a_n = 87n^3 - 76n^2 - 78n$

explicit \t recursive

Explanation:

An explicit sequence formula directly defines the nth term using only the index \(n\), without relying on previous terms of the sequence. The given formula \(a_n = 87n^3 - 76n^2 - 78n\) calculates \(a_n\) solely from the value of \(n\), so it matches the definition of an explicit formula. A recursive formula would require using prior terms (e.g., \(a_n = a_{n-1} + c\)) which is not the case here.

Answer:

explicit